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H I L O 








ESAGUL IE RS* LL 





Chaplain to his Grace the Duke of C HA 



Adorn d with Thirty-two Copper-P 



I" T^T7Tjg «aeaa3E 



a l °* ra *~ w -~~TiTTrr-iTi iii m i. 




Printed for John Senex, in Fleet ftreet ; W.Innys and Richard 
Man by, in St. Paul's Church-Yard } and John Osborn and 
Thomas Longman in Pater-nofter Row. MDCC XXXIV. 



TO HIS 



ROYAL HIGHNESS 

FREDERICK, 

Prince of WALES, Sec. 



SIR, 

TO contemplate the Works of G O D, 
to difeover Caufes from their EfFe&s, 
arid make Art and Nature ftibfervk 
fent to the Necemties of* Life, by a Skill in 
joining proper Caufes to produce the moft ufe- 

A % M 



D EDI CAT I O N. 

ful EfFe&s, is the Bufinefs of a Science, the 
Grounds and Principles of which, I have the 
Honour to lay at Your Royal H*ighness's 

Feet 

I have prerum'd to do this, Philofophy in 
all Ages having been thought worthy the 
Confideration of Princes 5 for the greateft and 
beft/ who have been handed down to us by 
HiftoriMs, under the rnoft amiable and glori- 
ous Characters, have diftinguifti'd themfelves 
by the%* Attammeiit^ in it, and^h^ Esicou- 
ragement of all Endeavours to advance and 
improve it. 

Amongft thefe I may juftly reckon his late 
Majesty, who was, and his prefent Maje- 
sty, who is, the Patron of a Society, erected 
for the Advancement of Natural Knowledge, of 
which one of their Royal Predeceflbrs was the 
Founder, 



Your 



D E D I C J T I O N. 



Your known Candor (Great Sir) will, I 
hope, excufe my plain Manner of treating this 
Subject: Tho' I take the Liberty to affiire 
Your Royal Highness, that I have fpared no 
Pains, that the Work might not be wholly 
unworthy of Your Patronage. 

It prefumes the more upon Your Counte- 
nance and Protection, as it is an Account of 
thofe Experiments, which I had the Honour to 
make fbme Years ago at Hampton-Court, be- 
fore his late Majesty, by his particular Com- 
mand y and as their prefent Majesties, who 
likewife honour'd thofe Experiments with their 
Prefence, have alfo given me Leave to fet their 
Names at the Head of my Subfcribers. 

Were I equal to the Defcription of thofe 
excellent Qualities, which make You the pre- 
fent Delight, and future, Hope of Britain i 
yet I mould be guilty of the higheft Indifcre- 
tion to attempt it in an Addrefs to Your felf - 



DEDICATION. 

iince none are more offended with Praife than 
thofe who moft defer ve it I fhall therefore 
no longer detain Your Royal Highness^ 
than whilft I beg Leave to fubfcribe my felf, 
with the greateft Refpeft, 

SIR, 

Tour moft humble, 
moft obedient, 
and moft dutiful Servant, 



J. T. D.E S A'GU L llRSa 



T H F 



AMES Of fuch 





S 



As have encouraged this 







BYT 





S C R I P T I 





late Majefty King George the Firft 

HIS PRESENT MAJESTY, 



&% r A u u : 



T MA JEST 



/ 



SUBSCRIBERS NAMES. 





A 



Llan, Mr. Lionel, Merchant 
^ ^ at Rotterdam 
Allen, Ralph Efq± P oft -wafer of 
Bath 

Anderfon, James D. D* 

Apreece, Robert Efqy 

Armftrong, Col. John Surveyor of 

his Majeftfs Ordnance 
Arnold, Robert, teacher of Maths- 

maticks 



B 



Aldwin, Samuel Efqy 
Barker, Mrs. Mary, of Broad- 
well in Glocefterfhire 
Baron, Rev. Charles A. M. 
Beal, John M. ZX 
Beaumont, Sir George Bart. 
Beeldemaker, Gerandus 
Bentinck, Rt. Hon. William 
Bernard, John, of Afhbury^ Efqy 
Bethel, Hugh Efqy 
Big, Rev. A. M. R W* Coll 
Billers, Sir William, Lord Mayor of 

London 
Blackbourn, William Efqy 
Bladen, Col Martin 
Blunt, Sir John Kt. 
Bond, Dennis Efqy 
Booth, Barton Efqy 
Booyaunt, Paulus 

Bornemannus, Philip Julius, of Hol- 
land 

Boyd, Mr. Robert 

Brace, J. Thurloe Efq\ 

Bradock, Mrs. Frances 

Branden, Peter Adrianus van dea 

Bridges, Brook Efqy 

Bridges, John Efqy 

Bridges, J— Efqy 

Brown, Mr. Thomas Merchant 

Brownlow, Rt. Hon. Lady E* 

Brownlow, William Efqy 



Buchleugh, His Grace Francis, Duke 0 
Bucler, Mr. John 
Buckenbourgh, Rt. Hon. Countefs of 
Burlington, Rt. Hon. Earl of 
Butler, Rt. Hon. Col. James 
Bute, Rt. Hon. James Earl of 



CApper, —^Efq % 
Carr, William Efqy 
Carpenter, Rt. Hon. Lord 
Cartwright, Thomas Efqy 
Cafwell, Sir George 
Chandos, His Grace James, Duke of 
Chamber, William Efqy 
Cheney, Rt. Hon. Lord 
Chriftophers, Theodore, Jan 
Church, Thomas Efq\ 
Churchill, Mr. Robert 
Churchill, Mr. Robert, Apothecary 
Churchill, Brig. Charles 
Churchman, Mr. Walter 
Gibber, CoWty Efq% 
Clarke, Rev. Samuel ZX IX 
Clare, Mr. Martin, School-mafeer 
Clements, Mr. John 
Cleaveland, His Grace Duke of 
Cobb, Rev. Dr. Ward. Winch. Coll 
Cobham, Lord Vifc omit 
Conduit, John Efqy 
Conway, Rt. Hon, Lady 
Cooke, Sir George Kt. 
Cope, Charles Efqy 
Corfini, Marq. Neri 
Collar, Thomas Efqy 
Coftar, Mr. John 

Colbe, Mr. J. L. Mathematical In- 
ftrument-maker 

Coladon, Efqy 

Collet, Dr. John 
Craufurd, Rt. Hon. Earl of 
Crop, Mr. Abraham 
Gumming, Sir Alexander Bart. 



Daniel 



5> 



SUBS C ft I B E R S NAME 8. 



D 

Ani'el, Capt. Hugh 
Dappe, Mr. John 
Darlington, Count ejs of 
Davies, Mr, Meredith 

Davis, Mr, ■> Shipwright at Am- 

fterdam 
Deering, Daniel Efy 
Dela Faye, Charles Efq\ 
Denune, Mr. George 
Dickinfon, Mr. Ezekiel 
Difton, Jo. Efqy 

Dobfon, Rev. J. D. D, Ward, of 

New Coll. 
Dobyns, Col. John 
Donnald, Mr. John 
Douglafs, George M. D. 
Dumford, Mr, Richard 

E 

EArle, Giles Efp 
Earle, Mr. Timothy 
Edens, Mr- Abraham Merchant 
Eden, Mr. John 

Edgecumbe, Rt. Hon. Richard Efp 
Edwards, Thomas Efq\~ 

Edwards, Efqy 

Edwin, Charles Efqy 
Eglinton, Rt. Hon. Countefs of 
Elliot, Mr. John 
Elliot, Sir Gilbert Bart. 
Elton, Mr. Abraham 
Everhard, Mr. John 

F 

FAirfax, Brian Efqs 
Fifher, Mr. Samuel 
Fizeaux, Mr. Jean 
Fletcher, Mr. Jofhua 
Folkes, Martin JS/j; 
Foreman, Mr. George 
Frederick, John Efg\ 



Furly, Mr. Benjohan Merchant 
Furnefe ? George Efq$ 

G 

GArnier, Monf. — - M. D* 
Gafcoigne, Mr. J — 
Gazola, His Excellency Count of 
Geelvink, N. Secret. 
Gibbs, Rev. Mr. John 
Girardot, John Efq- 7 
Golding, Mr. John 
Goodchild, Mr. John 
Gordon, Capt. George 
Gore, John Efqy 
Graham, Richard^; 
Greenway, Rev. William A. M« 
Greenwood, Charles Efqy 
Grove, John Efqy 
Grundy, Mr. John Surveyor 

H 




Ales, Rev. Stephen B. D. 
Halifax, Rt. Hon, George 



Earl of 
Hal], Stephen M. D. 
Halfey, Richard Efqy 
Hamilton, Lady Archibald 
Hamilton, Lady Margaret 
Hamilton, Mr. Archibald Merchant, 
Hanger, Mrs. Jane 
Harvey, John Ef& 
Hardwich, Dr. Peter 
Harford, Mr. Trueman 
Hawkey, Efcfr 
Heath, Ralph Efq\ 
Hays, Charles Efqy 
Haynes, Mr. Thomas 
Helot, Mr a John, Clock- maker 
Hepburn, Mr. John 
Herring, John Efq$ 
Hewet, Sir Thomas <KL 
Higgins, Dr. Abdias 
Hillsbourgh, Rt. Hon. -— Trevor 

Vifcount 

b Hooper, 




'S U B S C ft I B E R S A U E S. 



Hooper, Rev. Dr. Fkmcis 

Howard, Hugh Efqi 

Hunt, Rev. Dr. late Mafter of B. 

Coll.Oxon 30 Books 
Hum, Rev. A.M. V. P. of H.H. 

Oxon 

Hutchinfon, Rev. Thomas, A. M. 
Hutchirifon, John Efqy 

I 

J Ames, Mr. Thomas 
Jauniar, Rev. John f Chaplain fo 
his Grace the Duke of Grafton 
Ibervile, Marquis de 
Jefferies, John Efqy 
Jenkins, Tobias Efcfo 
Jones, William Efqy. 



M 

MAcclesfield, late Rt. Hon. Tho 4 
Earl of y Lord Chancellor 
Mack worth, Sir. Thomas Bart. x 
Mckenzie, Sir.*&e6rgc 
I^athfew, George Efa 
Mazeres, Peter Ef$ r 
Meads, Peter Ef%. 
Milbourne, George Efqy 
Middlemore,. John Efqy 

Milber t'Efo 

Mitchel, Mr. Henry 
Mole water, Baitiaeii Jun. , 
Montague, His Grace John Duke of 
Morgan, Mr. Johh, ofBriftol 

N 



K 



'Ent, Charles Efqy 
King, Mr. James 
Kox, Engil 

Kinglifrde, Mr. William 
Xrighout, Julius 
Kynafton, Mr. Thomas 





Ambert, 'Sir Edward 

Law, ~~ Efp 

deader, Charles, A. M>. F. N> 
Leigh, John Efqy 
Lippe, Rt. Hon. Count efs dela 
Lippe, Rt. Hon. Count dsla^ Sen 
Lippe, Rt. Hon. Count de la 9 Jun 
Loftus, Rev. Mr. Bartholomew^ 
Longfdale, Lord Vifcount of 
Lord, Robert Efqy 
Loup, Mr. William- 
Lufnew, — M.D. 
Lynflager^ Cap.Mmtj, 




Ewton, late Sir Uaac Kt. 
Niewaart, Cornelius M.D 
Nicholas, John 'Efqy 
Nicholfon, Henry M. D. 
Norfolk, His Grade the Ditke of 
Nourfe, Charles Efqy 
Nyevelt, Harm. Van Zuyle 




Glethorpe, James Efqy 
Qsborne^ : Sir John Bart. 




(Aiftey, Rti James Lord 
^ Parfons, , Col. John 
Pawlet, Rt. Hon. William Lord 
Pembroke, Rt. Hon.. Hen. Earl of 9 

two Books 
Phillips, Mr. Robert Bricklayer. 
Piddocke, Mr. Thomas 
Plumgtonj Richard Efq\ 



SUBSCRIBERS NAMES. 



Popple, Henry Efq% 
Price, William Efq% 
Price, Mr. John 
Pringle, John M I), 
Prude, Mr. Henry 
Purcell, Col. Martin 
Pye, Rev. Sir Richard 

R 

REdding, Col. 
Rippley, Thomas Efqy 
Riva, John Efq 7 
Robin, Mr. Pieter 
Rogers, Mr. Francis 
Rooke, George Efq 7 
Rouffignac, Guy M. D. Leffurer of 

Anatomy at Surgeons-Hall 
Rowel, Mr. John, Glafs-ftainer after 

the antient manner at Wickham 
R.ufhout, Sir John Bart. 
Rutty, William M D. 



Stanton, Mr. Ward 
Stephens, Mr. -~— 
Steel, Mr. Eugene 
Steighertahl,, — — M. D, 
.Stone, Mr. Arthur 
Strickland, Sir William 
Suffolk, Rt. Hon. Edward Earl of 
Suflfex, Rt. Hon. Talbot Earl of 
Sutton, Sir Robert Kt. 



T 

TAylor, Brook L.L.D. 
Tayleur, John Efa 
Thomond, Rt. Hon. Earl of 
Tobin, Sir James 
Trevor, John Efq, 
Trimble, Mr. Francis Merchant 
Truby, Mr. Richard, Jun. 
Tuffhell, Mr, Samuel 
Turbot, Richard Efq 7 
Tyrconnel, Rt. Hon. John Earl of 



V 




Almon, Dr. William Hairy 
Sambrook, John Efq 7 

Samuda M. D. 

Sands, Mr. William 
Senex, Mr. John, Bookfeller 
Shepherd, Mr. John 
Sherigley, Abraham Efq; 
Skreen, Richard Efq; 
Skipworth, Sir Fulwar 
Schelches, Mr. Andrew 
Sloan, Sir Hans Bart. 
Smith, Dr. Richard, 2 Books 
Snellen, Jan Van 
Southcoat, Philip Efq 7 
Stample, Mr. Peter, 
Stanhope, Charles Efq- 7 




'Alentinois, Due de 
Vanbrugh, Sir John 
Vaughan, Gwyne Efq*> 
Vincent, . Mr. William 
Vynor, Robert Efq 7 



W 



'Ager, the Hon. Sir Charles 
. , Walpole, Hon. Horatio. Efq j 
Wagg, Mr. Thomas 
Wall, William Efa- 
Wall, Mr. Tobias 
Weddel, Capt. Charles 
Wharton, His Grace Philip Duke of 




a 2 



Wharton 



SUBSCRIBERS NAMES. 



Wharton, George M. B« 
Wharton, Edward Jun. 
Wilkinfon, Andrew .Efq\ 
Woodcock, Thomas Eff 7 
Woodefon, Mr. — — 
Woodhoufe, Mr. William 
Wyndham, 7 Thomas Efq\ 

N, B. The Subfcribers are feftr'd to forgive any Mi/lake in their Titles^ if 
the fpelling of their Karnes, 




Wyndham 5 Sir- William 




Vonet ? John Paul Efy y 



P R E I A C E. 




P R E FACE 




L L the Knowledge we have of Nature depends 
upon Fads ; for without Obfervations and Experi- 
, ments, our natural Philosophy would only be a 
Science of Terms and an unintelligible J f argon. But then 
we muft call in Geometry and Arithmetic^ to our Afjiftance, 
unlefs we are willing to content our f elves with natural Hi- 
ft&ry and conjectural Philofophy. For, as many Caufes con- 
cur zn the Production of compound Effects, we are liable to 
mi/lake the predominant Caufe, unlefs we can meafure the 
Sztyantity of the Effects produced, compare them with, and 

them from each other, to find out the adequate 

Romance, by the Elegance of its Style and the flaujible Ac- 
counts of natural Phenomena, had overthrown the Arifto- 
telian Phyficks, the World rcceivd but little Advantage by 
the Change : For in/lead of a few Pedants, who, moft of 
them, being confcious of their Ignorance, conceal' 'd it with 
hard Words and pompous Terms ; a new Set of Philofophers 
flarted up, whofe lazy Difyoftion eafdyfell in with a P'hilo^ 
fophy, that required no Mathematicks to under f and tt; and 
who taking a few Principles jor granted, without examining 
tfair Reality or Conffteme witb e®ch other ? fancied they 




E F A G E. 

could folve all Appearances mechanically by Matter and 
Mt^ion; and, in their /mattering Way, fret ended to demon- 
fir ctiejfuch things, as perhaps Car tefius himfelf never be- 
lievd ; his Philofophy (if he had been in earneft) being un- 
able to ft and the Teft of the Geometry which he was Ma* 
flerof. 

Jt is to Sir Ifaac Newton V Application of Geometry to 
Philofophy, that we owe the routing of this Army of Goths 
.and Vandals in the ph 'tlofophical W wld ; which he has en- 
richd with more and greater Difcoveries, than all the 
Philof others that went be j ore him : A^hmlmd-fuch Foun- 
dations for future Acquijitions ; that even after his Death, 
his Works JliU promote natural Knowledge. Before Sir 
Ifaac., we had hut wild Guejfes at the Caufe of the Motion 
of the Comets and Planets round the Sun \ hut now he has 
clearly deducd them from the univerfal Laws of Attmffiion 
.(the Exiftmce of which he has provd beyond Contradiffiion) 
.and has JJjewn, that the feeming Irregularities <of the Moon, 
which Aftronomers were unable to exprefs m 'Mumbers, are 
but the juft Confluences of the Anions of the Sun and Earth 
Mpon it, according to their different Pofitions, His Principles 
dear up all Difficulties oj the various Phseiaomeiia of the 
"Tides \ and the true Figure of the Earth is now plainly 
pewn to be a flatted Spheroid higher at the Mquator than the , 
Poles, not with/landing many Affertions and Conjeffures to 
the contrary. Our incomparable Philofopher has difcover* 
ed and demonftratcd to us the true Nature of Light and Co- 
lours, of ubhich the mojl fagacious and inquifitive Naturalijls 
-were entirely ignorant ; for while they fought for the Origine 
of Colours m the Mixture oj Light and Shadow, Sir Ifaac 
Newton found that they were congenial with the Rays of the 
Sim, mid contained in Light it J elf, the Surface of colour d 

Bodies, 

1 



PRE F A C E. 



Bodies, fefvitfg m$y to feparath from owe another 'fhofe f&tffi.. 
that make different Colours \ by abfording forrte, and reflec- 
ting others to our Eyes ^ fa as fro produce thoje different Sen- 
fatibris, on which the pleafing Variety of colour d Objetis de- 
pends. Mis Opticks^ be-fides the Properties of Light, con- 
tain a vaft Fund of Philojbphy i which pho. he has modejl- 
ly delivered under the Name of Queries, as if they were,, 
only Conjedures) daily Experiments and, Qbfervations con- 
firm ; a notable Inftance of which may be feen in the Rev^ 
Mr. Stephen Halfe-V excellent Booh of Vegetable Statick%, 
which , by putting fever al of Sir IfaacV Queries out of all, 
Doubt y Jhe n Jb how /well they were founded. I pap over Sir * 
liaac Newtoii^ noble Inventions in pure Mathematicks y juflly , 
admired tit hoMe and abroad^ becaufe y thol they have be em, 
of great ufe in the Difcovery of the Caufes of natural Phe- 
nomena,, they are foreign to my prefent Subje6l 0 which is* 
iBhyficks ; whofe Knowledge I am, in this Courier endea- 
louring to, convey by Experiments y not only where Things v 
have been difcover d that way 0 but even where, they have 
been deducd by a long "Train of mathematical Conferences | ;i 
having contrived. Experiments^ which Step by Step bring us 
tothefameConcluflons. 

The Thoughts of being obligd to.Mnderflmd<M(Uhematichs^ 
have frighted a great many from the Newtonian Philofo- 
phy: I have hewd fever al Cartefians fay, that if the Know*?- 
ledge of Geometry was neceffary fo f their Convidion, they had * 
rather continue in their own Way ofPhilofophythan be at jo 
much Trouble ; as if a Man could defer ve the. Name of aPhi- 
lofopher^ merely becaufe he reafons jufllyfromBrinciples y when* 
thofe Principles are either apparently falfe, precarious, or af~ 
fumdat pleafure to ferve the j>refent, Pmpofe... It is not he 3 that 
canjbew from .em Hygothefl^ horn. we~ Cekjlial Motions 

might: 



PREF A C E. 



might be performed but he, that demonftrates their real 
Caufes, who gives a proper Account of the Syftem of the 
World: And it is the fame of other Phenomena ; for un- 
lefs w can demon/Irate 'what we explain, it is letter to own 
our Ignorance , than to endeavour to pafs our Conjectures upon 
the World for Solutions. If ever we come to know the 
Caufes of the various Operations of Magnetifm ; it will 
fooner be owing to a Comparison of the Experiments and Ob- 
fervations of Norman, Pound, Lord Paifley, Graham, 
Mufchenbrock, Savery, Marcel and others {who acknow- 
ledge themfelves ignorant of the Caufes of thofe furprizing 
Ejjctfs) than to. twenty Hypothefes of Men, whofc warm 
Imaginations fupply them with what may fupport their So- 
lutions, while daily Obfervations and common Laws of Mo- 
tion can eafily confute them. 

But to return to the Newtonian Philofophy ; tho its 'Truth 
is fupported by Mathematicks , yet its Phyfical Difcoveries 
may be communicated without. The great Mr. Locke was 
the fir ft who became a Newtonian Philofopher without the 
Help of Geometry ; for having asked Mr. Hoy gens, whether 
all the mathematical Proportions in Sir IfaacV Principia 
were true, and being told he might depend upon their Cer- 
tainty ; he took them for granted, and carefully examined the 
Reafonings and Corollaries drawn from them, became Mafter 
df all the Phjficks, and was fully convinced of the great 
Difcoveries contain d in that Book: Thus alfo he read the 
Optic ks with Pleafure, acquainting himfelf with every thing 
in them that was not merely mathematical. * But face 
Machines have been contrived to explain and prove experi- 
mentally what Sir Ifaac Newton has demonftrated mathe- 

* This I was told feveral times by Sir Ifaac Newton himfelf. 

matically, 



PREFACE 



matically, and fever al of his own Experiments are Jhewn 
inpublick Courfes,; a great many Perfons get a confideralle 
Knowledge of Natural Philofophy by Way of Amiifemcnt ; 
and fome are fo well pleased with what they learn that Way, 
ms to be indued to fiudy Mathematicks, by which they at 
lajl become eminent Philosophers. Dr. John Keill, was 
the fir jl who fublicUy taught Natural Philofophy ^Experi- 
ments in a mathematical Manner : for he laid down very ftm- 
fle Propofitions, which he proved by Experiments, and 
from thofe he deducd others more compound, which he f ill 
confirm d by Experiments ; till he had inflruBed his Audi- 
tors in the laws of Motion, the Principles of Hydrofta- 
ticks and Opticks, and fome of the chief Proportions of 
Sir Ifaac Newton concerning Light and Colours. He began 
thefe Courfes in Oxford, about the Tear ijo/^or 1705, 
and that Way introduced the Love of the Newtonian Philo- 
fophy. There were indeed, about the fame time, Experiments 
fhewnat London by the late Mr. Hauksbee, which were 
«le&rieal, hydroftatical, and pneumatical : But as they 
were onlyjhewn and explain d as fo many curious Phenome- 
na, and not made JJfe of as Mediums to prove a Series of 
philofophical Proportions Jn a mathematical Order, they laid 
no fuel Foundation for true Philofophy as Dr. Keill V Expe- 
riments; tho perhaps perform d more desteroujly and with 
a finer Apparatus.: They were Courfes of Experiments, 
and his a Gourfe of Experimental Philofophy. 

When Dr. Keill left the Univerfity, I began to teach 
Experimental Philofophy, after the fame Method that he 
had done, adding the Mechanicks (jiridly fo caWd, that is, 
the ^ Explanation of mechanical Organs, and the Reafm of 
their Epfis) Wy^WOptieaLPropofitions in my Courfes 
of Experimental Philofophy ; which ever fmce that time I 

c have 



P R E F A C E. 



have endeavour d to improve, by the Addition of ' new Propo- 
rtions and Experiments, and by altering and changing my 
Machines, as I found Things might be made more intelligible 
to fuchof my Auditors as were not acquainted with Mzthc- 
maticks, or more JatisfaBory to fuch as were ; efpeciaUy in 
what regards the Caufes of the Motions of the heavenly Bo- 
dies, and the Phenomena of our Syftem. About the Tear 
1 7 1 3 I came to fettle at London, where I have with great 
Pleafure feen the Newtonian Philofophy fo generally recei- 
ved among Perfons of all Ranks and Profefjions, and even 
the Ladies, by the Help of Experiments ; that tho fever al in- 
genious Men have fince that Time with great Succefs taught (and 
do flill teach) Experimental Philofophy in my (or rather 
■Dr.KeiHV) manner, I have had as many Courfes as I 
could pojjibly attend ; the prefent Cour fe, which I am now 
engagd in, being the iiift fince 1 began at Hart- Hall in 
Oxford, in the Tear 1710. The Satisfaction we enjoy by 
being any way inftrumental to the Improvement of others , 
is Jo great, that I cant help boa/ling — -that of eleven or 
twelve Perfons, who perform Experimental Courfes at this 
Time in England, and ' other Parts of the World, I. haste 
had the Honour of having Eight of them for my Scholars ; 
whole further Difcoveries become an Advantage to my felf- 
for what would raife Envy in any other Profejjjon, but that of 
a Philofopher, is receivd as a new Acauifition by all Lovers 
of Na tu r al K no wl edge, the Profit being fhard in common, 
while the Difcoverer has only the Honour of the Invention. 

For this Reafon, I never fcruple making Vfe of Machines 
and Inftruments contrivd by others ; nor was I ever fly of 
communicating, or even lending, my own, to thofe, who 
wanted to imitate themy it is enough to acknowledge the Au- 
thor of any new Contrivance, which I generally do. 



PREFACE. 



As thegreateft Part of my Auditors, at whofe Deftre I 
have printed this Courfe, arc but little versd in Mathema- 
tical Sciences ; the Le&ures are free from difficult geome- 
trical Demonftrations and algebraical Calculations ; and the 
fame thing is often provd by fever al Experiments ; that /where 
one does not immediately ft rike 'with a clear ConviBton, ano- 
ther ' may . I only require Attention and common Senje, 'with 
d very [ little Kt&hmetkk, inmy Readers, to qualify them 
for *mderftanding thefe Le&ures ; provided they begin the 
firft Lecture, and go on regularly, that they may advance 
from the eafieft Truths to thofe more complex ones, which are 
deduced from them; for other wife many things may feem dif- 
ficult to a P erf on, whojhould open the Book at random ; ef- 
pecially great Part of the loft Leaure of this Volume, 
which yet may be clearly underftood by all, who have made 
themfelves Mafiers of what goes before. Perhaps the Ma- 
thematicians may think me tediom and verbofe in my Lec- 
tures; but fuch of them as have been usd to teach, know 
very well, that one cannot be too plain and explicit with 
thofe that are not born with a Genius for Mathematicks 
{whatever good Under ft anding they are otherwife endow d 
with) nay jbmetimes one muft make Ufe of fuch Ways of 
demonstrating as are not mathematically true, to prepare them 
for "what is a little more abftratt ; as I have been often fore d 
to do to a large Audience, where clofe Attention is not very 
common. But 1 hope the rigid Philofophers will forgive 
me, when they find the fame Things geometrically demonftra- 
ted in the Annotations ; in the perufal of which, the Mathe- 
maticians perhaps will not think their Time wholly loft. 
However 1 dont mean to exclude common Readers from the 
Notes; for thofe that have carefully read and underftood the 
Lectures, will thereby be qualified for comprehending what is 
in the Annotations. € a 







— i a 



I Jlwuld now clofe this Preface, if the Largenejs of the 
Errata did not feem to want an Apology y hut after all the 
Care an Author can take^ mathematical Boohs have been of 
late fo incorredly printed, as to give the Reader a great deal 
of 1 rouble , and efpeciaUy young Beginners^ who are apt to 
attribute to their own Incapacity the Difficulty they find in 
Things 0 that are made unintelligible by the Printer s Fault ; 
therefore I rather chofe to offend the Eye y than puzzle the Un~ 
derjlanding y and when I was refolv d to rectify every Error y 
that might miflead the Reader, I thought it would be m weU 
to add a Page or two 0 and take in every falfe Pointing : Sa 
that if all the Faults be jirfl [ corfeBed wHh a Pen 0 according 
to the Direction in ihe%xt%£& r 
guzzle an attentive Reader. 

Bcfdes, to prevent the Publtch from being imposr ci v upm % 
I mufi not, omit mentioning^ that about f^teen v JTecvrS agp^ 
fome Per Jons publzjljed a Book ^ Experiment 
in my Name , without my Knowledge ^ which they endea-* 
vourd to pafs upon the \ World for my ' Le£lures^ ^ ^ 
thin Quarto , and was at that "Time calTd^ A Syftem of 
Natur al Pfiilofopfiy : And as thofe, who were capable of fuch 
a "Things may y very probably y if they have any of the Books 
left y endeavour to fell them by giving them the fame Title as 
my Bookj I thought proper to give this Caution, But while 
i am oomplaining of others^ 1 might be thought to ajcribe ta 
-my J elf what is not my own if I did not acknowledge \ 
that mo/I of what I have faid of the Bow and Spring in 
the lafi Le&ure of this Volume, as alfo Part of what I 
have faid of the Fly and the Battering Ram, was copied 
from fome. Papers lent me. by William Jones, Efq; 



Jhe READER is defied before he begim the Book r with Mt 

corrett the following ERRATA, 



Inflead oj 

Page 3 Lin. y of the Preface* abfirding 
2 13 Geometricans 
14 Structure, and j 
2 divided 

14 and 15 9. Befor^theAir £sfa. 



ib* 

4 
6 



10 
*3 

20 
21 
i£. 
22 
28 

36 
39 

60 
7° 

71 



72 

73 
74 



78 
83 

97 
1-05 

LO7 

1.08 
i.i 1 
1. 1 2 

xi 5 

X-2.5 

132 

3 ! 



m6 



1 7 # 1 8 its 

3 the Number 2:2 

Beginning of the Paragraph 
3 wi/^ 38. ^^/Jr^ If 
Antepenult known,., 

Caufes ; 
16 B o 
24 622! 

write in the "Margin 
7 Point Q_ 

At the End dele the 
overlooked, and 
Gravity of C : 
Center of Motion K 
A is the 
then 

probable 



2 7 
16 



1 1 

32 

33 
6 

14 

*9 

24 

32 

35* 
r6 

6 

27 



Time 



to carry as- 



24 Feet — 4! 
48 times lefs 
4 times in 
as troublefome 
B G, B D 
Diagonal 
AB^CD«. 
A B X F E : 
is M C 
fix Bodies 
dele and 
raifing 
antepenult from, the > 
1 o and 1 1 dele, whilfl the Body W 

rifes the Height B Z, 
23 C of the Arm D O,. 
the Plate, 
The. Screw 
In the 

So is the Weight : 



3° 
*7 

34 



3 1 

28 

35 
5 



»#. Powers, the 

3 Weights of their. 
21 Weight 

45. wnV* in the Margm 
12. Piece as Steel] 
*4 Eye ^ 
*6 fupports the E- 
24. C may 



abforbing 
Geometricians,, 
Strudlure^ Powers, and 
divifible 

9. If the Receiver had been perfeaiy full be- 
fore the Air was dtzwn m of it (tJta* thm 
their, . 



known r 
Caufes* 

62,2$ 
Fig. 18. 
Point O 

overlooked: And' 1 

Gravity of D : 

Center of Gravity K 

A is nearer to the 

than 

portable 

96 

48 Feet — ■ 24 Times 
24 times lefs 
6 times in 

more troublefome to carr$ thm 

BG, GD 

Hypotenufe 

AB-fCD: 

AB ~jr F E 

is equal to M C 

Jive Bodies 

riiing 

from that Part of the- 



C and the Arm D 
the Plates,,. 

61. The Screw 

62. In the 

So^ is the Weight : 

Powers (except the Wedge of 

is made) the 
Weights and their* . 
Weights; 

Plate 13. Fig, 12^ 
Piece of Steel 
Eye E<? 

fupports the Eye E ^ 



the Screw ■■■ 



R R A T A< 



171 



172 

173 

176 
177 

179 

*8x 
183 

1 85 



88 
■*9 



237 
241 

246 
250 
252 



3 



256 

258 

260 
261 
2.66 

*75 



1 z 
29 

3° 



hpadqf 

P. 136 L. 25 Piece C. 

A B with 
Pi oe E F 

Wire K k as far as h 
and the Weight 
of which D 

the Weight w ; the WeightW 
P and p. 
£ and at 

draw E C - to C D 



139 
168 



X69 
170 



19 

16 

7 
u 

1 1 

32 



4 
4* 



all the Paragraph The 
firft &c. confjiing of 8 
and #z « r 



16 goes thro* 
penult. Weight : : 
29 Rub at g 1 



28 
27 
28 
10 
16 
21 
24 

23 
3° 
3i 

33 

2 

3 1 

3 
8 

3° 
36 

3J 
18 



of the Weight 
farther from 
nearer, 
this Force 
DD is 
of one th 
is one 1 th 
Bafe B C $ 
of a c 9 
one 30th 
100 lb. 
PL 14. 

dele more than 
of a Leather 
Direction a D 
Wheel F 
124,16 lb. 
in all 21,41 Ounces 
to draw 1 40 lb. 
up Hill 



28 for that the Fly 
28 the Gudgeon 
then the 
it will add 
Prim. 
19. Fig. i. 
IP 

uk. having brought 
ult> Pofition H L 
j 6 the Board to 
antepenult. Rolator 
3 1 about the Stone 
19 top Ropes 
25 Fig, x* 



38 

4* 
12 

28 

17 



Piece C f . 
A B, with 
Pioe EH 

Wire H k as far as D 

and the Weight, and their Velocities 
of which C 

the Weight w ; the Weight w 
PandP). 
h m and a n 
draw E c — to C b 



and 0 Cr 

The Weight (taking in the Weight of the 

Wheel) ; 
goes perpendicularly thro* 
Weight of the Wheel and what it carries - • 
Rub » at g, fuppofing the Wheels of the feme 

Weight 
of the Velocity 
nearer to 
farther. 

this Force of the Weight 
Bd is 0 
of one 1 2th 
is one 12th 

Length of the Plane A B 
of Af 

a little more than one 30th 
a little more than 100 lb. 
P * I > 1 7 • 



of Leather 
Direction AD 
Wheel D E 
124,61 lb. 

in all 2 1 355 Ounces 
to draw 240 lb. 

up Hill, when his Weight is made 



ufc "of 



and therefore he goes the flower, 
for the Fly 
the other Gudgeon 
then let the 
and it will add 
Prifm 
20. Fig. 10. 
F P 

having brought his Legs 

Polition h L 

that the Board mould 

Rotator 

about the Hammer 
top Rope 
Fig. 1 and 2, 



revolts 



tl AT* A 

XV J\. A JL M.9 



Jnjhad of 



read 



P. 275 

278 
282 



283 



286 

287 
291 

293 
296 

297 

301 

3°3 
304 

305 



310 
3 1 1 
318 



3^0 



L. 31 

19 
6 

9 

37 
16 



321 
3 2 9 



330 



345 
34 6 

3'49 

355' 



357 

361 

362 



revolts 
Section 

after Additions 

D C; at D big enough 

W (Fig. 6.) 

of third 



ult. after £3V« 

34 the Line A B 

35 the Line A b, becaufe 
15 Point D but 

2 F/§\ 2. 
in the Margin— -PI. 24. F. 2. 

ult. fuppos'd it to make ; the 

26 bac, 

26 1 a?, which 

26 uniformly diminiuYd 
28 uniformly accelerated. 

27 re&ineal 
24 rife to % 

penult, join by a String to the 

4 Diftances of 

6 that is, the 

7 the fbur- Ounce Ball 
4 The 2d Figure 

21 The Weights 

26 — in a Second 

3 5 Diagonal E/ 
30 Force fhou'd - 

penult by half. 
ult. but the half : 
1 9 its Fall is 
9 31 Miles. But 



from A toVB; 
2 and 3 advance towards the 
Center of the Earth no 
2 X after than A G 



8 great than its Gravity , 

30 the former Area 

16 one another,.,, when* 

20 8 Days longer 

31. going- off, 

35 to A, 

37 down to p>, 

3 8 quit at B 

21- Action, or equal 

21, AG.and.B... 

22 the Part Baft 

26 . up from /. 

12 and the contrary 



revolves 

Profils 

But the firft Hint was from Mr 9 Gw® G?&h@ffi* 
DC at D, big enough 

?f the third 
J. B. The gth Figure is only pari of tki %t& 
Figure drawn larger* 
the Line . A b, 
the Line A B, becaufe 
Point D over againffc him,, but 

Fig. I. 

PI. 24. F. 1. 

fuppos'd it to make the 
b a, c k 

ix, Severally parallel to thofe Tangents^ whack 

continually diminifhU 

continuall y accelerated , 

rectilineal 

rife to 3 

joyn, by a String, the 

Diltances of the Centers of 

that is the Center of the 

the Center of the four-Ounce Ball 

the 3d. Figure 

9. The Weights 

N n B * ? We f on '* con f ider m y Flaficity that tb$ 
Body might have. 

Diagonal E f 

Force ( -fuppofing k now diminiuYd In the Pro- 

portion of L 2 to L k) Ihould 
by near half 

but a little more than half 

its Fall (confidering Gravity only as a Blow) is 

3 1 Miles ; and partly, becaufe the Increafe of 

v c ^ lfu S al Force deftroys more of the 
the Action of Gravity near the Equator 
than towards the Poles, But 
from A to H 

advance upon the Plane no 

N.B. A more Geometrical Solution of this may 
be found in the 37 th Theorem of Dr. John 
Ketllm his Introduttio adveram Phyficam, 

greater ftill, ~ 

the former Area 
one another, even when 
8 Days fhorter 
going offs 

down to B 
quit it at p» 
Action, are equal 
AG and BF 
the Part <T 
up, to./, 
and the fame. 



m R R- i T A 



R 368 L, 



37* 
374 



379 
.381 



38* 

389 

39 1 
405 

418 



436 
445 



n 
26 

28 

18 

29 

7 

22 



Inflead 



Southern Regions 
Water as high 
have as high 

from the Center £ round t to 
together, every other Stroke 
Pivion 
Barnouillii 



penult, and e D 1 fo 



Second Page 374. lin« zo, about 

Hours 
20 the Body's 
28 from C to 'A - 
30 lateral Motion, 



11 

l 7 
3* 
5 

24 
2 

9 
23 

1 2 
35 



a Man carried 
all the Diftance 
Perihelia be D E I 
PI. 28. Fig. 11. 
15 _ T T Paris Feet, 

Ball '= b == lb, 
as 15630. 
25630 

28 Degrees, and of 5 48 
dele at Full 



read 

Southern Regions in the oppofite Months 6 

Water nearly as high 

have nearly as high 

round the Center b from 0 to 

together every other Stroke, 

Pinion 

Bernoulli 

and e D ; but more efpecially, becaufe the 
Tangents are every where parallel to the 
correfponding Chords : 

about 10 Hours. 

the Spring's 
from G to A, 

lateral Motion of the Parallelogram in -which. 

he is plac'd . 
a Man at B carried 
at the Diftance 
Perihelia be D, E ; 
PI. 24 F. 1 1 . 
1 5 _L Paris Feet. 

Ball = h = 24 lb, 

as 15630==* 6400 X 2,4. 

15630 

about 28 Degrees, and of Q about 48 



of the Index Alpheb et ical Alphabetical 



Subscribers NAMES omitted. 



Betenfon ., Sir Edward, Bart, 
Bowles, Mr. John 
Brooks, Mr. Thomas 
Chetwind, William E/q; 
Frederick, Thomas, Efp 



Glover, Phillips Efq\ 
Holland, Mr. John 
Hog, Mr. Roger 
Matthew, Capt. William 
Page, Thomas Efp 



Page, Hon. Mrs. 

Preis, His Excellency Joachim, 

,! ' r derick 
Reyna Ion, Samuel EJq; 
Zolicofre, Theod. William Efq, 




HE RE AS fome Booh fellers have declared \ that 
as foon as my Courfe comes out, they will get it tranf 
lated into French (as cheap as they can, no (iouht^ left my 
Booh Jhould he ffioil-d hy cm hafiy, and perhaps ignorant Tranf- 
lator, I intend to translate it my felf having already done 
more than half; and if any other 'Tranjlation appears, 
fh all write my Name in each Booh with my own Hand 
that my foreign Auditors may not he impofed upon. 



O F 





HILOS 





LECTURE I. 




H E Spirit of Diluting, and an earnefl: Defire to 
obtain the Vi£tory, rather than come at the Truth, 
has been one of the greateft Impediments to the 
Improvement of natural Knowledge. And nothing 
occafions more wrangling, than when different Per- 
fons annex different Ideas to the fame Words ; for 
Men can never rightly underftand one another, till they mean 
the fame Things by the fame Expreffions. No Difputes arife in 
pure Mathematics, becaufe the Definitions of the Terms are pre- 
mised ; and every Body that reads a Proportion has the fame 
Idea of every Part of it : So that when any Man is fo weak as 
to think to bring one Dempnftration in oppofition to another, he 
is to be difregarded by every one that wou'd reafon like a 

B Philor 




2 A CowJe of Ex 

LecY I Philofopher : For we may immediately put an End to all Ma- 
' thematical Controverfies, by fhewing, either that our Adverfary 
has not ftuck to his Definitions, or has not laid down true Pre- 
mifes, or elfe that he has drawn falfe Conclufions from the Prin- 
ciples' he has laid down ; or at leaft own, that we do not under- 
ftand fome Part of his Demonftration, and defire him to explain 
it : for unlefs we can fliew where the Error or Paralogifm. is, , we 
muft not condemn by the Lump, but acquiefce with him in 
hat he has prov'd. 

I t is true, that in mix'd Mathematics, where we realon ma- 
thematically upon Phyfical Subje&s, we cannot give fuch juft 
Definitions as the Geometricans or Logicians do : We muft be 
content with Delcriptions, and they will be of the fame Ufe as 
Defini-ions, provided we are always confident with our felves, 
and always mean the fame Things by thofe Terms, that we have 
once explain'd : For to lay, that others have taken the Words 
we ufe in a different Senfe, can be no valid Objedion ; be- 
caufeit may be anfwer'd, that then they meant not the fame 
Things as we do. Therefore in this Courfe, when we make 
ufe of fuch Words, as have been varioufly underftood, we fttall 
fhew the particular Meaning, in which we wou'd have them ta- 
ken : And when we are oblig'd to coin new Terms, as it will 
often happen in the Defcription of Machines, we fliall always 
explain them the firft Time they are mention'd. 

1. B y the Word Matter we underftand all that has Extenfion 
and* Refiftance : And becaufe all Bodies, whether folid or fluid, 
are extended and do refill:, therefore we fay, that all Bodies 
are made of Matter. 

2. The Cartefians wou'd have Matter to confift in Exten- 
fion alone ; but Extenfion without Refiftance is nothing but 
mere Space. For tho' they affirm that one cannot have an Idea 
of Extenfion without Body ; it is contrary to Experience : 
Since if we take a Cube out of a cubic Box, which it exadiy 
filfd we may very eafily conceive the Length, Breadth, and 
Depth of the empty Box ; and it muft be a fecond Idea, that 
Will give us a Notion either of fome other Body coming in to 
fill the Box, or of its Sides coming together by the Preffure of 
ambient Bodies. ■ 

3. 1 HAT 




J e of ' MLXperttnentm rmiojopby. 5 

g. That Matter is die fame in all Bodies, is evident from 
its Definition ; tho 1 the common acceptation of the Word 
wouM give us another Notion; for in our common Difcourfe 
we fay, an Infirument of Wood, Brafs, tfrlron, or of any other 
Matter, as if the Difference of Bodies confifted in their different 
Kind of Matter : Whereas all Matter is homogeneous, or of the 
fame Nature in all Bodies, whether folid or fluid, hard or foft, 
more or lefs heavy ; whether they belong to the Earth, or any 
other Part of the Univerfe ; as for Example, the Matter of Cork 
does not elfentially differ from the Matter of Fiefh, or that of 
Gold or Diamonds. But the whole Variety of Bodies,* and the * Ann. u 
different Changes that happen in them, entirely depend upon 
the Situation, Diftance, Magnitude, Figure, Stru&ure, and Co- 
hefion of the Parts that compound them. 

4. That Mercury refills more than Water % and W ater more * Anne 2 » 
than Air, is not owing to the one being of a more refilling Mat- 
ter than the other ; but to the greater Number of Particles con- 
tained in the fame Space in the heavier Body ; and often to the 
ftronger Cohefion of Parts ; and then a lighter may refill more 
than a heavier Body, to a Force imprefsM to feparate its Parts ; 
as Wood will refill: more than Water, and a Diamond more than 
Gold. But where there is little or no Cohefion of Parts, even in 
the fubtileft Fluids, we find a Refiftance : For Light condensed by a 
burning Glafs, tho 7 many thoufand Times rarer than Air, has a 
■confiderable Refiftance, as appears from its feparating the Parts of 
Bodies, fo forcibly, and fo loon, when they are plac'd in the 
Focus of the Glafs : Nay, and when the Rays of Light are as 
much difpers'd as they are here on Earth, coming directly from 
the Sun, they have a fenfible impelling Force, as appears by ob- 
ferving, that the Vapour arifing from a Comet (which makes 
its Tail) is always driven toward that Side- of the Comet, which 
is oppofite to the Sun ; and that happens whether the Comet 
be going towards, or coming from the Sun, even at Diftances e- 
qualto, and greater than that of the Earth. And if there be 
a Medium finer than * Light (as we have Reafon to believe from* A ^3. - 
fome Phenomena) even that Medium has a Refiftance, whereby 
it refra&s, refle&s, and bends the Rays of Light near the Surfaces 
and Sides of Bodies* 

B 2 5* 




Le£h- I. 

\^v^ 5. T h A t Quantity, and confequently Matter, is divided in 
f Ann. 4. Infinitum *, has been feveral "Ways demonftrated by Mathemati- 
cians ; and one cannot conceive a Particle of Matter ever fo 
finally but what is ftill divifible ; for fmce it is a Body, it muft 
have a Top, a Bottom, and a Middle, unlefs we fuppofe the Top 
and Bottom to be the fame, which is abfiird'; and if fo, we may 
conceive fuch a fmall Particle to be divided in the Middle. But 
then we are not by fuch a Divifion to imagine the Parts to be 
feparated from each other, any more than (when we divide a 
cubic Space of two Inches into eight cubic Spaces of an Inch,) 
thofe new Cubes are to be fuppos'd removM from each other, 
or taken out of the two Inch Cube which contains them. 

* Ann. 5, 6. As to the a&ual Divifion of Matter * by feparating the 
Parts from each other, it is not poffxble beyond a certain Degree ; 
becaule there are Atonies ^ or extremely fmall Parts, which are 
calPd the constituent or component Parts of natural Bodies^ 
which the Wife and Almighty Author of Nature did at firft create 
as the original Particles of Matter, from which all corporeal Na- 
tures were to arife, that are without Pores, folid, firm, and im- 
penetrable perfe&ly, paffive, and moveable : So that the utmoft 
Mechanical Divifion that we can arrive at, does only feparate 
fome of thefe firft Parts from one another, and alter their Con- 
ta£fc ; for mixM and compounded Bodies are deftroy'd by fuch a 
Separation, and not by breaking the original Particles to Pieces. 
Thefe primary Particles being perfectly folid, muft be much more 
hard and firm than any Bodies that can be made out of them 
with Pores or hidden Vacuities interfpersM, that is, fo perfectly 
hard and firm, that they can never be worn away or diminftfd : 
For 'tis not reafonable to fuppofe that there fhould be any Force 
or Power in the ordinary Courfe of Nature, that can divide that 
into feveral Parts, which God in his firft Creation of Things has 
made One. As long therefore as the original Particles remain 
entire, there may for ever be Bodies made or composed o^them^ 
which fhall have the fame Nature and Texture : But if thefe 
could be broken j worn away or diminijhed^ then the Nature of 
corporeal Things, which is dependent on thefe, might be chang- 
ed, Earth and Water composed of either fuch Particles as have 
been worn or broken, or of their Fragments* could not have, 



A Courfe of Experimental Phihfophy. $ 

at this D ay, the fame Nature and Texture, as that original Led. I. 
Earth and Water, which was compos'd of thefe Particles when w^Vv 
they were found and entire. Wherefore that the Nature of 
Things fhould laft, and their natural Courfe continue the fame 
all the Changes made in Bodies muft arife only from the various 
Separations, new Conjunctions and Motions of thefe original 
Particles. 

7. These muft- be imagined of an unconceivable fmallhefs * - } * Arm*. 
but by the Union of feveral of them together, there are made 
bigger Lumps or Parts of the firft Compofition (as they are 
call'd) which have Interftices between them, becaufe the firft 
Particles do not touch in every Part of their Surface ; and thofe 
Interftices are call'd the Pores of the firft Compofition, Like- 
wife by the uniting of feveral of thefe Lumps there are form'd* 
Molecular or Lumps of the fecond Compofition, which have 
Pores of the fecond Compofition, larger than the former : And 

fo on to the feveral Compofitions before we come to Bodies of a 
fenfible Magnitude. Hence it follows, that there muft be a great 
deal of Vacuity * interfpers'd in all Bodies, according as they are * Ann. 7. 
made up of fewer or more Compofitions ; and all Spaces are not 
equally full of Matter *. This will be plainly {hewed by an Ex- * Am, 8„ 
periment. 

Experiment i. Tlate 1. Fig. 1. 

8. Upon B the Brafs Plate of the Air-pump (which we fhall 
hereafter defcribe) fet a tall Cylindric Glafs-receiver A B open at 
both Ends of about five Inches Diameter and feven or eight 
Foot high. Let it be made Air-tight by Means of a wet 
Leather upon the the Plate B, and another upon the Mouth 
of the Receiver A under the Covering Plate D, to which 
Plate underneath is fcrew'd the Machine Tsj>s contriv'd for 
letting fall Bodies in Vacuo at the fame Inftant of Time. 
For when the Wire W (which flips to and fro thro' the 
Collar of oil'd Leathers r, that the Air may no way efcape) 
is _ drawn up by its Hook h, the fquare horizontal Plate > 
being brought up to a narrow Part of the Brafs Springs^ & 
caufes them to open fo as to let the Plate P (moving on an 
Hinge) fall into a vertical Pofition; upon which the Bodies, 
that were laid 011 it drop at the fame Moment, T hex* 



Xe£h X Then upon the fquare Plate P lay a Down Feather, and 
ijTSi^sJ a Guinea juft by the Side of it, (See Pig. 2. where the Plate 
P is in an horizontal Situation,' as it refts on the Return of 
one of the Springs s, and the Collar c is feparated from the 
covering Plate and Springs, thro' both which it muft be fcrew'd, 
when on the Receiver) and having exhaufted the Air from the 
Receiver ; by pulling up the Wire w let the Guinea and Fea- 
ther drop, which falling both with the fame Velocity (as at 
C) will come to the Bottom at the lame Time: But if the 
Air had not been exhaufted, the Guinea would have been at 
Bottom before the Feather had falPn a quarter of the Height 
of the Receiver/ 

9. Before the Air was drawn out of the Receiver, if it 
had been perfe&ly full (tho' then there was much more Vacu- 

* Anno 9« urn * than Matter) yet it is evident, that there muft be a great 
deal of Vacuity in it, after the Air is pumpM out; becaufe 
.the Refiftance is fo far diminifli'd, that the Feather falls at 
leaft four Times fafter than it did in the common Air. For 
whatever fine Air was left in the Receiver ; whatever Particles 
of Light, or whatever fubtile Effluvia penetrate the Glafs, and 
get into the Receiver; all that Matter, is much lefs in Quan- 
tity than the Air taken out, becaule the Refiftance is diminiflf d« 
For to lay, that after Exhauftion the Receiver is as full as be- 
fore, wouM be as abfurd, as to fay, that a Gallon of Beer turn'd 
into Froth (fo as to reach from the Bottom to the Top of the 
Receiver) fills it as full as eight Gallons of Beer without Frothy 
which it is capable to contain. 

10. Gravity may be lookM upon as a Property of Mat* 
*er, which tho*' not effential, is yet univerfal, and in one Senfe 
■infeparable from it; that is, all Parcels of Matter, however modi- 
fied, (or all Bodies) have a Gravitation or Attra&ion towards one 
another ; as will be hereafter demonftrated in Refpe£t of heaven- 
ly, as well as terreftrial Bodies : The Tendency of heavy Bo- 
dies towards the Center of the Earth, being owing, to the 
fame Caufe, that makes the Sun and Planets tend towards one 
■■•another N B. When , we ufe the Words Gravity, Gravitation, 
or Attraftion; we have a Regard not to the Cau/e^ but to the 
>Effe£f s namely to that Force, j which Bodies have when they are 

-carried 




ourfe of Experimental Philoppfy j 



carried towards each other ^ which fat equal diftancesj is al- Le£L I* 
ways proportionable to their Quantity of Matter ; whether it k^y^j 
be occaflon^d by the Impulfion of any fubtile Fluid \ or by any 
unknown and unmechanical Tower concomitant to all Matter* 

1 1.. If all the Matter in the Univerfe was contained in two 
equal Balls or Spheres, placM at feme Diftance from each o- 
ther ; thefe Spheres wou'd move towards one another with e~ 
qual Velocity, lb as to meet in the middle of their firft Di- 
fiance. But if the Spheres be fupposM unequal in any Pro- 
portion; they wouM meet in a Point as much nearer the great 
""all, as the great Ball wouM be bigger than the other. 



12. The Reafon why we do not perceive this mutual At- 
traction in fuch Bodies as we daily handle, is, that our Earth 
having infinitely more Matter than thofe Bodies, attracts them 
fo ftrongly as to make their mutual Tendency towards each o~ 
ther infenfible. So it happens in refpe£t of a Load-Stone and a 
Piece of Iron; which when let fall at a little Diftance from one 
another, do not appear to move towards each other ; tho 7 we 
find their Effeft fenfible when brought near together. 

T h is will be illuftrated by the following Experiment.:, 

Experiment 2. Tlate 1. Fig. g. . 

Upon the Table TAB fet the two Balls A, B, equal 
in Bignefs and Weighty (for Ex. of two Ounces each) at the 
Diftance of a Foot from the Hole C, and two Foot from 
each other. Now if the Earth was annihilated, or was re- 
moved to an infinite Diftance, and the Table did not attract, 
the two Balls wouM come to each other and meet at C ; but 
Gravity 9 or the Attraction of the Earth, preffing them againft 
the Table, they remain at reft; but to overcome that Prefc 
fure, and make them aft as if the Earth was away, let 
a String of about go Inches long be tied to the Ball A, 
then brought thro 7 the finobth Hole in the Table C, then 
round the Pulley under the Table, and fo up again tliro^ 
the Hole C, and at laft faftenM to the Ball B. Let the W eight 
P of four Ounces hang from the Center of the Pulley D: 
Then if you let go both the Balls , at the fame . Time, they 




Le£t. I. will come to each other equally fall and meet juft over the 
v^v^ Hole, 

i If inftead of the Ball A, yon fubftitute another, which 
weighs but one Ounce (whether it be lefs than the other, or as 
big, but hollow, or of light Wood) and this Ball A be let 
go from the Diftance of one Foot, and the heavier Ball B from 
the Diftance of fix Inches from the Hole (hanging three Ounces 
at the Pulley) they will both meet again at the Hole, the 
lighteft Ball going thro' twice the Space that the other does. 

14. In the firft Cafe, the Quantity of Matter in the two Balls, 
which is four Ounces, being confiderM as divided into Two, caufes 
a two Ounce Ball on each Side to move towards the ..Hole, 
which confequently move thro 5 an equal Space in the fame 
lime* 

15. In the fecond Cafe, the Quantity of Matter which is 
three Ounces, being divided into Two, does on one Side v caufe 
a Ball of two Ounces to move towards C, and on the o~ 
ther a Ball of one Ounce to move towards the other, which laft 
moves twice as faft, becaufe it has but half the Quantity of Mat- 
ter, weighing but half. 

Aim. 10. N B. Any JVetght may hang to the Tulley^ * provided it be not 
too light ; becaufe it only ferves to overcome that Gravity ^ which 
J?r effing the Balls againfi the Table v, hinders them from moving to- 
wards each other / as they wou'd do^ if the Earth did not exifij 
or was removed to an infinite "Diftance. 

16 . If the Ball B be fupposM infinitely greater than the Ball A, 
the Velocity of the Ball A will then become infinitely greater 
than that of the Ball B, fo that B will ftand ftill and A move 
thro 0 the whole Diftance between A and B ; the whole Quantity 
of Matter belonging to both, being now wholly attributed to B 
alone, and A looked upon as a Point without any fenfible Quan- 
tity of Matter, and confequently unable to move the Ball B by 
its AttraQion. This is applicable to the Earth and all the Bo- 
dies about it, which in refped of them is look'd upon as im- 
moveable, whilft they, as fo many phyfical Points, move in the 
Lines defcrib'd by their Centers of Gravity, as they fall to the 

Ground 



A Courfe of Experimental PMkfophy. 

Ground, without having any Regard to the Quantity of Mat- Led 
ter, which they contain, whereby they attraft the Earth towards v^*v 
them. Thus alfo fince the Sun contains almoft 230000 Times 
more Matter than the Earth, this hit is look'd upon as a Point 
defcribing an EUipfis about the Sun, call'd the Magnus Orbis, 
whilft the Sun, that attracts the Earth, is confider'd as immove- 
able in one of the Foci of that Elliplis : Or rather the Moon and 
Eartlr together may. be confider'd as reduc'd to one Point, which 
is their common Center of Gravity, and which defcribes the Or- 
bit abovementioned. 

17. T h e Earth in relpe£t of the Bodies about it, and the Sun 
in refpe£t of the Planets and Comets, and all the Planets in re- 
fpe& to the Satellites and other cir&umambient Bodies, do exert 
a greater or; Mer Force of Attradion, according as the Bodies 

are nearer or farther off; for Gravity, * being a Virtue diffused* Ann. 
from an attrading Body every Way in right Lines, decreales 
in the fame Manner as all other Virtues propagated from a Cen- 
ter roundabout. So Light and Heat become weaker, as we re- 
cede from the lucid or hot Body- This Decreafe of Virtue is 
in a reciprocal duplicate Proportion of the Diftance ; that is, at 
twice the Diftance, the Virtue is four Times weaker, and at three 
Times the Diftance, nine Times weaker, &c. Thus for Exam- 
ple, if the Earth was three Times farther from the Sun, it would 
be nine Times lefs -attracted, nine Times lefs enlightn'd, and 
nine Times lefs heated than it is at prefent : In like manner ; if it 
was four Times farther, it would be fixteen Times lefs aife&ed 
by thofe Qualities. So on the contrary, if it was three or four 
Times nearer than it is now, it wou'd be nine or fixteen Times 
more afFe£ted. 

This Proportion of Increafe or Decreafe of Qualities diffused 
every Way, may be illuftrated by the following 

Experiment g. Tlate 1. Fig. 4. 

18. Ta k e a Candle, fo fmall that its Rays, that are diffused 
every Way, may proceed as it were from one Point ( for if the 
Candle be large, its Light muft be made to pafs thro 5 a fmall 

Hole in a Paftboard) and if a Cube * of an Inch, as A, be held* Ann, u 
up upon a Needle, at the Diftance of one Foot from the Can- 

C die. 




Le,&; die, its- 'Shadow- will cover the Surface of a two Inch Cube B % 
v^n^ held at the Diftance of two Foot from the Candle, which laft 
Surface is four Times larger than that of the firft Cube,^ as ap- 
pears by applying the firft Cube upon the bit. Hereby it is e~ 
vident, that if the firft Cube was twice as far from the Candle 
it would receive but the 4th Part of the Light ; and 'but the 9th 
Part, if it was three Times as far ; becaufe when held at one 
Foot from the Candle, its Shadow will cover a three Inch 
Cube held three Times as fan In the fame Manner will a 
Sphere of an Inch Diameter at one Foot from the Candle in- 
tercept all the Light, which wou'd fall upon a two Inch Sphere 
at two Foot, or a three Inch Sphere at three Foot from the 
Candle, their Surfaces being as 1, 4 and 9, proportionable to 
the Squares of their Diameters* 

19. A s it is eafier to raife moft Bodies from the Ground than 
to break them in Pieces ; that Force by which its Parts cohere, is 
ftronger than its Gravity. That Force, whatever be its Caufe, 
we flhall call the Jbtrattion of Cohejion. This Attraction is 
ftrongeft, when the Parts of the Bodies touch one another; 
but decreafes much fafter than Gravity, when the Parts that 
were before in contaQ:, ceafe to touch ; and when they come to 
be at any fenfible Diftance, this Attra&ion of Cohefion becomes 
aim oft inlenfible. 

This Attraction is always the ftrongeft, where the Contact 
is the greateft. As for Example, two Boards of Fir or Oak, be- 
ing glued in the Middle along the Grain, are not fo eafily broken 
afunder in the glued Place, as any where elfe ; becaufe 
there are more Pores, and confequently fewer touching Parts, a- 
long the Wood any where elfe, than where the Glue is ; for when a 
joint is fhot (as the Workmen call it) or the two Pieces of Wood 
made fmooth, in order to join them, the Glue which is fpread on 
the Pieces fills the Pores; and caufes the Wood not only to touch 
where it did before, but even in the Interftices where it did not 
touch ; becaufe thofe little Spaces are filPd with Glue, that fupplies 
the Place of Wood, On the contrary, when the Wood is more fo~ 
Ann. 13. lid, * or has fewer Pores than the Glue, it does not hold fo faft 
where it is glued, as in the other Parts of the Wood ; which may 
be feen in Brazil-wood, Ebony, or Lignum- vitae, and in Metals* 
The Parts, of Glafs, which are almoft round, touching but in a few 

Points 




'ourfe of Experimental Phihfophy. t 



Points, are eafily feparated, and therefore it breaks eafily : And Left. I 
Fluids (whofe Parts feem to be Spherical) have fcarce any Co- w^v^ 
hefion, except fo much as ferves to make Drops, whofe Roundnefs 
plainly proves an Attraction of Cohefion : For if this Roundnefs 
depended upon the Freffure of the Air, the Drops wou'd not be 
round in Vacuo ; and if it depended upon the external Fref- 
fure of any other Fluid whatever, two Drops coird never unite 
into one ; becaufe the Figure of any Portion of a Fluid * prefs'd* Ann. i& 
every Way, by the lame or any other Fluid, cannot be altered by 
that PrefliiFe ; whereas from a mutual Attraction of the little 
Globules * that compofe the Drop, it muft become round ; and it * Am r?« 
will continue fo, becaufe then there will be the greateft Conta£fc 
poffible between all the Parts* A Drop of Water, or any o~ 
ther Liquor, does indeed become flat where it touches a Table, 
or any plane Body, that does not repel it ; but this is owing to 
the Attraction of the Table, and to the Gravity of the Drop, if 
the Table be horizontal. 

How fuch an Encreafe of Contact increafes this Attraction^ 
is more evident by the following 

Experiment 4* Tlate x. Fig. 5. 

20, Having moiften'd or thinly fmearM over with Oil of 
Oranges * two Glafs Planes A B C D, (18 Inches long, and three * Allru t -& 
or four Inches broad) lay them upon one another in an horizon- 
tal Pofition in the wooden Frame HILM, having firft put a 
Drop of the fame Oil upon the under moft Plane at G, and laid 
a thin Plate or Piece of Money upon the faid Plane, between 
D C, to hinder the upper Plane from touching it at that End 
whilft their other Ends A B are in clofe Conta£h The Drop 
being large enough to reach the upper Plane, will immediately 
be flattened and move on towards the touching Ends, continu- 
ally increafmg its Diameter, as at (V and R, and likewife mov^ 
ing fafter as it fpreads. Nay tho' the Planes be raisM up at 
their touching Ends by means of the Prop ^ O N, the Drop will 
continue to advance towards the touching Ends, but not fo 
faft* When the Drop is at G, a fmall Elevation of the Planes 
will retard it ; if they be raisM a little higher, it will flop ; if 
ftill higher, the Gravity of the Drop will ad more ftrongly 
than the Attra&ion of the Planes, and make the Drop move 

C 2 down- 



1 2 A Courfe of Experimental Phihjbphy. 

Left. I. downwards towards C D. When the Drop is at Q^ 9 the Plane: 
LAAJ will require a much greater Elevation to flop the Drop, or make 
it move downwards ; and ftill a greater when it is at R. Now 
when the Planes are rais'd fo. high as to make the Drop run 
back; if the. upper Plane be prefsM by the Finger a little above the 
Drop fo as to come nearer to the lower Plane ; the Drop will 
not only ftop, but move upwards ; becaufe it fpreads more by 
that PrefTure. and touches fo many more parts of the Glafs 
than it wouM have done, that even at this Elevation of the Planes, 
their Attraction overcomes the Gravity of the Drop. That it 
moves at firft towards A B, is owing to the greater Attraction 
of the Planes at e, where they are nearer together than at f; and 
*Ann. 17. that the Velocity of the Drop encreafes, is owing to its moving 
towards A B, where the Attraction muft encreafe continually *■ 
as the Planes come nearer and nearer* 

Several other Circumftances of the Attraction of Cohefl- 
on are fliewn by the following Experiments. 

Experiment 5.- Tlate ju Fig. 6«. 

21. Having fix'd into a piece of Wood or Cork C C 9 
ieveral little Glafs Tubes, the Diameters of whole Bores are 
lefs than one another, (the biggeft being about * r of an Inch) 
let the Ends of thofe Tubes be dippM into any ting'd Liquor 
that will adhere to Glafs, as red Water ; and the Liquor will 
fpontaneoufly rife in all of them, but always higheft in thofe 
whofe Diameter is leaft ; as appears at 1, 2, g, 4? 5v when 
they are dippM in the red Water of the VeileL A B. 

In very fmall capillary Tubes, the Liquor will rife very high, 
but then the Colour will be imperceptible; But. to make the 
rifing Liquor vifible in that cafe, the Tube may be applied 
to ones Finger after it is prick'd lb as to make a drop of Blood 
ilfue out, which will rife very quick and be vifible tho' the 
Tube be as fmall as an Hair. See Tlate 2* Fig. i. 

A n y porous Body will have the Effe£l of capillary Tubes : 
thus Water will rife up into a piece of Bread ? or into a 
piece of Loaf Sugar whofe lower end. is dippM into the Li- 
cjuor; but it will rife much higher into Lckf Sugar, ; becaufe 
its Interlaces are fmaller than thofe of the Bread 



Jt Courfe of ^Experimental PMoJophy. . 13 

Le£t L 

Experiment. 6. 'Plate 2. Fig. 2. v-orx-i- 

Take two fquare Planes of Glafs A B C D and Having 
moiften'd them with Water, fet them upright in a Veffel of 
the fame Water, prelEng the Sides together at A B 5 but keep- 
ing the oppofite Sides D C afunder by putting a thin Plate 
between them* The Water will rife between the Planes in 
the Curve efg, where it is to be obferv'd that the Fluid 
always goes higheft where the Planes are neareft, namely; to- 
wards A juft as it happens in the fmall Glafs Tubes. 

That none of thefe Phoenomena arile from the PrefTure of 
the Air, is evident byonaking the Experiments in Vacuo ; which 
may be eafily performed by means of the Wire w (Tlate 1. 
Fig. 1.) which can move up and down thro' its Collar of 
Leathers without admitting the external Air into the Recei- 
ver, as it rifes or deprelfes the Planes or the Tubes faften'd, 
to it. The whole, ^££aratm for this will be hereafter def~ 
crib'd*. 

Experiment. 7* Tlate 2. Fig. gv 

23. In a clean Ghfs that is not full, Liquors will be higher 
at A B where they touch the Glafs than in the middle C; 
but that Elevation is hardly fenfible but near the Sides, be- 
cause the Attraction of Cohefion reaches but a little way. 
Quickfilver does the reverfe in this cafe; and; in fmall Tubes 
it does not rife fo high as the Surface of the reft of the Quick- 
filver in the Velfel in which the Tubes are held. The Reafon 
of thefe Phoenomena * is, that Water is attra&ed by Glafs* Ann. xb* 
more than it is attracted by it felf ; and that on the contra- 
ry, Quickfilver, attracts Quickfilver more than Glafs attradsit* **Ann..i9- 

Experiment 8. Tlat f e 2. Fig. 4.. 

Let A B be a Cylindrick Glafs VefTel filPd up to the 
Line A B ' with -Quickfilver, whofe Surface is loweft at A and 
B the Sides of 'the-. Glafs, where it rifes with a Convexity,. 
If an open Tube of a fmall bore D E be prefs'd againft the 
infide of the. Glafs (to render the Experiment vifible) its lower 

Orifice:, 




Xe£t.'L Orifice being almoft at the Bottom of the Glafs, the Mercury 
^wo^rs^ will rife in the faid Tube no higher than F below the Sur- 
face A B of the Mercury in the VefTeh But to avoid all 
Cavils about fomething in the Tube that might be fuppos'd 
to ftop the Mercury, let the Experiment be made in this Manner : 
Let the Tube being quite full of Mercury, (and kept fo by the Fin- 
ger prefsM on the upper Orifice D,) be put into the Veffel, whole 
'bottom is a little convex, below the Surface of the Mercury as 
low as E ; upon the removal of the Finger, the Mercury in the 
Tube will fall below F, and then rife above it, and after fome Vi- 
brations fettle at F, the Point to which it rofe before* 

Experiment 9. TlaU 2. Fig, 5. 

24, I n t o the Cylindrick Glafs Jar A B of about 5 Inches 
Diameter and 1 f Inch deep pour gently about one Pound 
of Quickfilver, and a circular part of the Bottom as C G 
will remain uncovered ; then if you fliake the Jar to make the 
Quickfilver come together, the whole Bottom will be cover'd ; 
but if without any fhake you continue to pour on more Mer- 
cury you may put in a Pound or two more before the Bottom 
be quite cover'd, the Pit C C becoming continually lefs, but 
deeper ; and if then you bring the Mercury together to cover 
^he bottom and deftroy the Pit; a Finger being pfefs'd againft 
the Bottom thro' the Mercury, will, when taken away, leave 
a Pit as before, the Mercury there remaining convex at the 
Sides of the Pit; as appears in the vertical SefHon of the 
Clafs and Quickfilver in the lower Figure 5* Tiate 2* 

Experiment 10. . Tlate 2. Fig. 6. 

if* Having put in ftill more Mercury 'till there be no 
dPit left, lay a piece of Iron Wire C C about two or three 
Inches long and of an Inch thick upon the Surface of the Mer- 
cury, where it will fwim making a dent on both Sides as at 
O; "which happens becaufe the Mercury attra&s itfelf more 
than it does the Iron; fo in the cafe of Fig. 5. it was lefs 
attracted by the Glafs than by it felf, and therefore made the 
Pit ; but when once the Sides of the mercurial Pit C C 
were brought to touch, they never .parted again of themfelves 0 



A Courfeof Experimental / Philqf&pBy^ 



Experiment xx. Tlate 2. Fig* j. 

26. I £ ^ m reprefents the Surface of the Mercury, and tlie: 
"ire which fwam at the Top be prefs'd down to the Bottom,., 
(Jwhere D reprefents its tranfverfe Section,) the V/edgesof Mer- 
cury b c a f that go under the Wire fo as very nearly to meet ; 
at c 9 will not remain in their places, but by the reft of the 
Mercury they will be attracted towards d, fo as to leave 
the Spaces he a without any Mercury; as appears in the Sec- 
tion of the Glals, "Wire, and Mercury, Fig. 8., And that 
it is lb in fa£t, appears by looking at the under fide of 
the Glafs in the upper Fig. 8. where the Wire or Wires, 
(if there be more than one) become vifible thro' the Bottom*, 
of the Glafs, which cou'd not be unlefs the Mercury went 
away from under them; becaufe a Cylinder can touch a Plane 
but in an invifible Line: And as a farther Proof of this; the 
Wires, tho* fpecifically lighter than Mercury, remain at bot- 
tom, as being prefs'd only downwards by the Arch of Mer- 
cury over them ; which cou'd not happen if the Mercury cou'efi 
infinuate it felf under. 

37. N o w if the Experiment be made with a Silver Wire 
of the fame bignefs as the Iron one, when it is laid at top r 
the Mercury will rife up round it as at a a. Fig. 9. and 
this Wire will not remain at the Bottom of the Glafs tho* 
pufh ? d down to it, but always emerge, neither does it become 
vifible thro 5 the Bottom of the Glafs, tho* held down againfk 
it with the Finger; nay even when the Finger is feen on each 
fide of it. This happens becaufe Silver attracts Mercury more 
than Mercury attracts it felf But to fhew that this Attrafti- 
on is only ftrong in Contactor extremely near; let the Sil- 
ver Wire be made a little foul by putting it into the Fire,, 
and then the lame thing will happen to it as to the Iron Wire ; 
becaufe the Attraction of Cohefion is infenfible, at the Diftance 
of the Thicknefs of the thin Skin that there covers the Silven 

28., That there fhouM be a Conta£t to bring Bodies to 
cohere very much, is evident from the foldering of Lead or 
rafs with a Mixture of Lead and Tin, commonly callM foft 

S ol de 1 o , 



Led, I. Solder. For if thefe Metals be not well clean'd, they can never 
v-^-v^w. be folder'd jperfeftly tight ; and in Lead, after the Parts that are 
to be joiri'd have been made foul by rubbing them over with 
Chalk, and then with Mallows or any Green-Herb, fo as to 
make a thin Skin; the Work-Man fcrapes clean the two Edges 
of the Lead that are to be join'd, that the Solder may come 
clofe enough to the Metal ; and when the Solder is "pourM on 
hot out of a Ladle, then fpread with an Iron, it fattens ftrong- 
ly where the Metal was clean'd, but does not at all ftick where 
the Skin remains that was made by the Chalk and Juice of the Mal- 
lows. It has been obfeiVd that the Air alone will foul or make a 
Skin over the part of the Lead that has been clean'd, and therefore 
Greafe or Tallow is commonly rubb'd on after {"craping; for the 
Parts of any fat or inflammable Subftances being much finer than 
thofe of Air, will allow the Solder to come much cloler to the Lead 
than a Plate of Air, or what leparates from the Air to ftick to the Lead. 

29. In what Proportion of the Diftance this Attraction of 
Cohefiori encreales or decreafes is not yet fully known ; but 
from fome Phenomena, we have Reafon to believe that it 
decreafes in a biquadratic Ratio of the encreas'd Diftance ; that 
is, at twice the Diftance it acts 1 6 times more weakly, and 
at 3 times the Diftance 81 times more weakly, &c. For it be- 
comes infenfible at the leaft fenfible Diftance. 

30. There is in Nature another fort of Attraction not lb ftrong 
as the Attraction of Cohefion, but ftronger than Gravity ; whole 
Proportion of Decreafe, in the Removal of Bodies Attra&ing, is 

Ann. 20. near ly as tne Cube and a quarter of the encreas'd Diftance : * 
And this is the Magnetical Attraction. As for Example, if a 
Loadftone attracts a piece of Iron with a certain Force at a 
given Diftance ; at twice the Diftance, the Attraction will be 
10 Times weaker: And at three Times the Diftance, the At- 
traction will be 33 i times weaker. But as Magnetifm is a 
particular Virtue that affects only Load-ftones and Iron and 
Steel, we fhall refer a fuller Account of it to another Place- 
becaufe we are now only confidering general 'Properties of Bo- 
dies. We fhall only obferve, that the Load-ftone repels as well 
as attrafts ; for that Pole of the Stone, which attrads one End 
of a touch'd Needle, will repel the other. 

31. There 



A Courfe of Experimental Thilqfiphy. j j 

3 1 . T h e r e are feveral other Inftances in Nature of a repellent <W"%i 
Power in Bodies * ; and very often the fame Bodies that attract* a nnot 2 
one another at certain Diftances, and under fome Circumftances, 

do repel one another at different Diftances, and under other Cir- 
cumftances. . 

This may be feen upon the Dilfolution of Salts in Water;, 
That the Parts of the Salts attract one another, appears from 
uniting into hard Lumps when the Water is evaporated, fo that 
the Particles come fo near to each other, as to be within the Pow- 
er of the Attradion. That they repel one another at farther Di- 
ftances, appears from the regular Figures into which they coa- 
lefce, when by the Evaporation of part of the Fluid in which they 
float, they are brought within each others Sphere of Attraftion • 
thefe regular Figures depending entirely upon the Equality of their 
Diftances one from another before this Evaporation, and this Equa- 
lity of Diftance being owing to an Equality of repelling Force. 

32. A repelling Force is alfo prov'd by the Production of Air 
and Vapours ; for thofe Particles which are forc'd out of Bodies 
by Heat and Fermentation, as foonasthey are out of the Sphere of 
Attraction of the Bodies, do immediately recede from them, and 
from one another with a great Force, and avoid coming together 
again ; fo as fometimes to take up above a Million of Times the 
Space which they did before in a denfe Body. 

33* The Attraction and Repulfion in the fame Body at a confi- 
derable Diftance, is evident in feveral electrical Experiments. 

I F you rub a Piece of Amber with a dry Hand of a woollen 
Cloth, it will put into motion Threads, Feathers and light Bo- 
dies, attracting and repelling them at a Diftance : And therefore the 
Name otEletfricity has»been given to that attracting and repelling 
Force which is excited in any other Body by the fame Friction as 
is given to the Amber. Wax, Rofiri, Sulphur, Silks, Paper, 
Ribbons, Hair, and Feathers, and feveral other Bodies have this 
Property : But Glafs has it more than any other. 



I 



ACourfeof Experiment a 




Led. I. 

v^tn) Experiment 12. Tlate 1, Fig. ic. 

24 Take a Glafs Tube of about \ \ Inch Diameter, and rub- 
bins it from one End to the other with a dry Hand pretty briskly, 
it will attrad a Feather, or any light Body, at a confiderable Di- 
ftance, from one to eight or ten Feet. After a Feather has been 
attraded and ftuck to the Tube for fome time it will fly oft of 
it felf, and never come to the Tube again (which conftanty repels 
the Feather in the Air, whenever it is brought near it) till it has 
touch'd fome other Body ; as a Finger or a Stick. And it the 
Finger be held pretty near the Tube, the Feather will alternately 
fly from the Finger to the Tube, always ftretching out its Fibres 
the way that it is going, and that before it comes oft from, the 
Finger or the Tube. In driving the Feather about the Room with 
the Tube j it mufi now and then be rubb'd afrejh to excite the Ele- 
flricity, which continually grows weaker > after the Friction is 
over. 

Experiment 13. Tlate 1. Fig. 11. 

•i< If feveral little Pieces of Leaf-gold, or Leaf-brafs be laid 
uponaftand or fmall Table, and the rubb'd Tube beheld over 
them at the Diftance of a Foot or two ; the Pieces of Ixar-gold 
will move from the Table to the Tube with great Swiftnels : And 
often by the Attradion and Repulfion they will move backwards 
and forwards without touching either the Tube or the Table. 
But if two Books, or two Pieces of Wood of the fame Size be fet 
up on End on the Table on each fide of the Leaf-gold, as at 
A, B ■ (Tlate 2. Fig. 12.) fo that their Diftance AB be equal to 
the Height of one of them : Then the Tube being held between 
their Tops, as at D, will have no Power to move the Leaf-gold, 
tho 1 the Diftance from the Leaf-gold be but fix Inches, when 
the Tube juft before attraded the Leaf-gold at a Foot or two ; but 
if the Pieces of Wood be removM, without giving the Tube a new 
Fridion, it will attract and repel the Leaf-gold as before. When the 
Pieces of Wood are not remov'd, the Tube will not put the Leaf- 
gold in Motion, till the Diftance D C from the Tube to the Gold 
be lefs than half the Diftance A B of the Pieces of Wood : As if 
this EfFed could not be produc'd while the Sphere of Attraction 

■ reprefen- 



A Courfe of Experimental Philofophy. ip • 

reprefented by the Circle ECF (wliofe Center is in the middle of Left, t 
the Section of the Tube at D) is difturb'd by the Pieces A 
End B» 

Experiment 14. T Hate 2. Fig. ig* 

36* T o know when the Tube is fufficiently rubb'd to make 
Experiments with it, you muft move your Fingers ends nimbly 
by the Tube, as if you went to ftrike it in a Direction perpendicu- 
lar to it's Axis, but the Fingers need not come nearer than a quar- 
ter of an Inch from the Tube: Then the Effluvia or fine Parts that 
fly from the Tube will fnap again!! the Finger^ or (beating back 
from it) againft the Tube, fo as to be heard with a Noife like 
the crackling of a green Leaf in the Fire ; but not fo loud. 

According to the State of the Air, the Tube requires more 
or left rubbing. In Weather that is hot and moift, the Tube re- 
quires a great deal of Friction before it will fnap, and attract and 
repel the moft ftrongly ; and then at beft it's Virtue will diffuie 
it felf but a little Way : So that the lame Tube, which in dry cold 
Weather gave Motion to the Fibres of a Feather at the Diftance of 
eight or ten Feet, will fcarce a£t fenfibly at the Diftance of two 
Feet when it rains in Winter. 

I f the Tube be warm'd at the Fire without rubbing, it will 
have no EfFe£l : It's Ele6tricity will alfo be left if you rub the 
Tube long enough to make it very warm ; and then you muft let 
it cool before you ufe it again. \ 

It is not amift to let the Tube or any Glaft to be rubb'd before 
the Fire to dry it before you ufe it, especially if it be pretty thick, 
provided it is not much heated* 

37. I t is remarkable, that if the Tube be rubb'd in the dark, 
the Effluvia will appear lucid ; and when it is made to dap (as in 
the 13 th Fig. of Tlate 2.) there appears a Light upon the Fingers 
Ends, as at A ; and if a little Brufh be held near the Tube, as at B ; 
or drawn along it without touching, juft after it is rubb'd, Sparks 
of Light like Stars will appear upon every Hair of the Bruih ; but 
the fame part of the Tube will not fnap or give Light twice toge- 
ther in the fame Place without a new Friction. * Annot. 22. 



Ex PER I'* 



ACourfeof Experimental y Thihfop> 



B.XE.ERIM.E.NT i$, T late 2. Fig. 14. 

Is the rubb'd Tube be brought near a Down Feather tied to ; 
the upper part of a little Stick (landing upon a Foot ; the Feather 
will ilretch out its Fibres towards the Tube ; but upon the Ap- 
proach of a Finger be.tween the Tube and Feather, they : will 
be repelPd by the Finger ; tho' they will be again attracted by it 
as foon as the Tube is removed ; and then the Fibres wilL turn 
back again to the Stick and be attracted by it,, when, the Finger 
is taken away. 

Experiment 16., T late 2^ Fig. 15. 

■39... If you fet a Glafs. Receiver, about five Inches wide, and 
twenty Inches high^ over the Stick and Feather, having firft dried 
the Receiver at the Fire or in the Sun ; upon rubbing the Glafs 
with one or both Hands from Top to Bottom, the Feather will 
ftretch its. Fibres every way like the Radii of a Sphere, when the 
Hand is removed from the Receiver. But if whilft you rub the Re- 
ceiver, or after rubbing, you only move the Hand upwards and 
downwards, the Fibres of the Feather will (notwithftanding the 
Interpofition of the Glafs) follow the Motion of the Hand : And 
if the Tube be rubb'd within a Foot or two of the Receiver, the 
feather in the Receiver will likewife follow the Motion of the 
Hand rubbing the Tube. When the Tube has its Ele&ricity ex- 
cited by Fri&ion, if it be brought *near the outfide of the Re- 
ceiver, the Feather will ftretch its Fibres towards the Tube ; and 
upon the Removal of the Tube turn back to the Stick \ though 
fometimes this laft Phenomenon will happen at the approach of 
the Tube, and the Fibres will ftretch out again when the Tube 
is taken away : Nay,, fometimes there feem to be Fits of Attra- 
ction and Repulfion ; for whilft the Tube is held near the out-fide 
of the Receiver, the Fibres of the Feather will be alternately ex- 
tended and contra&ed^ without any new Fri&ion given to either 
of them, 

40. Just after the Receiver has been rubbed, if you Blow to- 
wards the Feather, ( See the 1 5th Fig. Tlate 2.) its Fibres will 
fly from the Blaft ; and they will alio fly from an Hand mov'd 



A Courfe of Experimental Pbildfopfy g f 

briskly towards the Glafs, yet fo as not to touch it ; but the Ex-Le£h ... L,.. 
periment wilLnot do twice without rubbing the Receiver a-new, 

41.. Most of tliefe Experiments^ if not all ? „ will fucceed even 
when the Air has been pumpM out of the Receiver : Only 'there 
will be this difference, upon rubbing it in Vacuo, that the Light 
excited will be of a Purple Colour, in a much grea ter Quantity, 
and all within the Glafs : And whereas Bodies would be attracted 
before, when held near the outfide of the Glafs, now that Power 
will ceafe, and the Virtue will exert it felf wholly inwards. The 
fame will happen to the Tube when exhaufted, as alfo to a Glafs 
Globe * whirPd by Means of a Wheel, and fo rubbM by the Hand ;* Annoys- 
as is defcribed more at large by the late Mr. Hawkshee in his 
Book of Experiments, where he has given a large Account ofia 
great many electrical Experiments that he made* 

4.2.. Ifhall fay no more on this Subje£t now ; becaufe I fhail 
liav:e Occafion to confider it more fully in another Part of my 
Courfe : And the Intent of this Lefture is only to fhew,— That 
thole Properties of Bodies, fuch as Gravity, Attractions, and Re-? 
pulfions, by which we fhall hereafter explain feveral Phaenomena, 
are not occult Qualities or fuppofed Virtues, but dp really exift, 
and are by Experiments and Obfervations made the Obje£ts of our 
Senfes. Thele Properties produce Effe&s, according to fettled 
Laws, always acting in the fame Manner under the fame Cir- 
cumftances : And, tho^ the Caufes of thole Caufes ^ are not 
known, fince we do not reafon about thefe hidden Caufes ; it is 
plain that we reje£t occult Qualities, inftead of admitting them 14 , 
our Philofophy, as the Qartejians always objed to us, . 




X But the whole Variety^ &c] 

Annotat. TT F we confider the Bricks of which a Building confifts, as its Imalleft or 
Ixft. I. 1 firffc Parts j we iliall find that, however fimilar they -are, their different 
s^x^v^o ' A Diipofition, in relpe£t to each other, will produce very different Parts 
of the Edifice : An Arch, a Wall, a Chimney, a Peer, a fquare or a 
round Pillar, a Globe or a Cube are compos'd of the lame Sort of Bricks ^ 
and fuch as ferved for one Part, when pulled aiunder, will as readily lerve 
for another. So in the wonderful Edifice of the Univerle, there is no need 
of a Difference in the Atoms or firft Particles, of which the feveral Parts 
*are compounded : The" fame Atoms being as proper to make Land as Sea^ 
to make Gold as Clay : And, when we do not confider the Soul that actuates 
the Matter, a particular Diipofition of the firft Atoms makes all the Dif- 
ference betwixt a lifelefs Lump, and the Body of a curioufly organized 
'-Animal. 

One may bring various Examples of Matter trac'd through feveral Bo- 
Bodies, whole Changes depend upon the different Texture and Pofition of 
the Parts. 

When the Water of Rivers, Seas,- and Lakes, Is lb rarified by the Heat 
of the Sun, as to become fpecifically lighter than Air (which will happen, 
when it takes up above 900 times the Space in Vapour that it did in Wa- 
ter) it will rife up lb high as to form Clouds of various Colours, which 
.float about at that Height, where the Air is of the feme ipecifick Gravity 
as the Clouds. 

When the Winds, by carrying off lame of the Air above, caule that 
■iwhich is below to become Ipecifically lighter. by its Expanfion m 0 the Clouds, 
retaining the fame Ipecifick Gravity as they had before, do then defend, 
4tnd, by the Refiftance which they meet with in their Defcant, are chang'd 
"into Rain, which falling down to the Earth, does in a great JVIealure run 
±>ack into the Rivers and Seas \ but fome Part of it runs into the Earth, 
and is imbibed by the Seed of Plants. If we confider ib much of it as gets 
ifito the Grains of Wheat that are ibwn, the Appearance of.it is much 

♦chang'd 



A Courfe of E^erimental Philofophj. 2 g 

chang'd in the green Blade of Corn, then in the Straw, afterwards in Annotate 
the Ear, and in the Grains contain'd in it. The Wheat, by being ground Left. I. 
in the Mill, puts on the Form of Flour j which being made up into Pafte <s^v~^ 
and then baked, is again changed into the Cruft and Crumb of Bread. The 
nourifliing Parts of the Bread (after it has been eaten by Man, and has 
pafs'd thro' the Stomach) do out of the Inteftines pals thro 5 the Lafteal 
Veffels into the Receptaculum Chyli, and thence up the Du&us ( Thoracicus 
into the left Subclavian Vein, or (as an ingenious * Anatomift has lately Mr. St. m~ 
difcovered) into the left internal jugular Vein j where mixing with the fa. 
Blood, it goes along with it thro 5 ' the Heart and Lungs, where it receives 
vivifying Particles from the Air, and returning into the Heart, is from 
thence by the A£Hon of the left Ventricle of the Heart, and the Arte- 
ries carried to the 'Extremities , of the Body. There fome Part of this 
new Blood circulates back again ; whilft other Parts are changed into the 
Subftance of Bones, fome into Membranes, fome into Hairs, ibme into 
Nails j and other Parts of it paffing thro' the Glands, are turn'd into Sweat 
and fo become Water again, as at firfl:, 

If we had confider'd fuch Drops of Rain as impregnated Linfeed j 
We might have trac'd it thro' the Stalks of the Plant, Flax made of that> 
Thread fpun from the. Flax, Linnen made of the Thread, a white Pulp 
made of the Rags of the worn Linnen beaten up with Water at the Paper- 
Mills, Paper made of that Pulp thinly fpread upon a fine Net- Work of 
Wire 5 and laftly the Smoke, which burn'd Paper affords, is again eafily re- 
duced to Water. 

Solids become Fluids, as Metals do by the Aftion of Fire, or being diP 
fclv'd in acid Menftruums 3 and Fluids put on the Form of Solids, as Mer- 
cury will be made hard by the Fumes of Lead : And two Chymical Li- 
quors will immediately upon their Mixture coalefce into a firm Sub- 
ftance. 

It is to their particular Figure that Machines and Instruments owe 
their Ufefulnefs - 0 Clocks, Mills and other mechanical Engines being on- 
ly valuable, when their Parts that are made to communicate Motion have 
their proper fitnefs. 

The iame kind of Glafs produces great Variety of Effects, according 
to the different Figure of its Surface - 7 as is known to all that have feeri 
Optic Giaffes. 

The Difference of Seafons which makes fiich changes on the Surface of 
our Earth, and even in. the Bodies of Animals, is entirely owing to the' 
different Situation of the leveral Parts of the Earth in Relpeft: to the: 
Sun. 

Thole that would read more upon this Subject may ■consult Dr. John KeiPs 
Imroduftio ad veram Phyficam. Edit. 3, Left, 7* 




^Annotat. 5. [4. That Mercury rejifts 9 '8cc. m ] Mercury weighs 1 3 f Times more than 
.Left. X Water, and is found to refill juft 13 j Times more:, and Wa er which weighs 
w^V^n^ between 800 and 900 Times more than Air, is found to refift juft lb much 
more. This Sir Ifaac Newton found by making Experiments upon Pendu- 
lums of Wood and Lead in the Air, Pendulums of Lead in Water, and of 
Iron in Mercury. See his Principia y Edition 2d. Book 2. Prop. 31. and 
Prop. 40. where he demonftrates that the Refiftance of Fluids is as their 
^ Quantity of Matter. 

I made an Experiment before the Royal Society about two Years ago 
with a Ball of Gold of an Inch Diameter - 0 which, being llilpended by a 
String,, did firffc ofcillate in Water and then in Mercury : And it appeared 
that 42 Vibrations in Water deftroy'd as much of the Motion of the Golden 
Pendulum as three Vibrations in Quickfilver. And letting the Ball of Gold 
fall in a Copper Tube four Foot long, and 4 \ Inches Diameter, filled with 
Mercury (from an Height of three Foot ten Inches) and nicely obferving 
the Time of its Fall, I found by comparing leveral Experiments, that 
the Refiftance of the Medium (difcovered by the Method taught in the ~ 
faid^th 'Prop, of the Principid) agreed fo exa&lywith Sir Ifaac Newton's 
Theory, as not to differ one Tenth of an Inch in the Space that the Ball 
fell thro 5 , which was three Foot ten Inches, 

3 ^<\—And if there he a Medium finer than Light , &c] See Sir Ifaac 
Newton's Optics, fecond Edition, Book 3d. Queries 18, ip 7 20 and 21. 

4. Zi—>7%at Quantity , Sec. is divifible in infinitum, Of the many 

Demonftrations brought to prove this AlTertion, I fliall only mention two 
that are very plain and obvious. The firft taken from Dr. s 7 Gravefande'sln- 
trodu&ion to Sir Ifaac Newton's Philofophy, Part 1 ft, No. 18. 

Plate 3+ Fig. 1. 

Let there be a Line A D perpendicular to B F, and another : as'G H at 
a Imall Diftance from A, alio perpendicular to the lame Line. With the 
federal Centers C, C, C, &c. and Diftances € A, C A, &c defcribe Cir- 
cles cutting the LineG H in the Points e. &c. The greater the Radius 
A C is, the lets is the part e-G. Since the Radius may be augmented in * 
-'infinitum, therefore 'the 'Part eG may be diminiih'd in the lame Manner j 
and yet it can never be redue'd to . nothing, becaufe the Circle can never 
coincide with the right Line JB E. 

The next is from Dr. JohnKeil's IntrdduUio ad veram Phyfi Lec. 3, 
De Magnitudinum Dhifibilitate. 

Let AB (Plate?. Fig. 2.) be a Perpendicular between the Parallels 
-C D, E F. From the Point C in one of the Parallels draw the Line C G 
Co a Point G on the other Parallel on the other fide of the Perpendicular 

AJ§£ 



ACourfe of Experimental Philofophy. 2$ 

A B, and it will divide the faid Perpendicular into two Parts at K: Ano- Annotat. 
ther Line drawn from C to H will divide the Part K A (of AB) into Left. I. 
two Parts j and fince upon the Line E F, which may be produc'd i/z Infini- ^^y^ 
turn, other Points as I, may betaken, new Lines may ftill be drawn to 
divide the remaining Part of A B. For whatever Line is drawn from C 
to any Point of the Line E F, however diftant, it can never coincide with 
the Line CD; and therefore it will ftill divide the Part of AB that re- 
mains after the foregoing Divifion. 

For other and more ample Demonstrations, See the laid Left. 3 d. 
where he alio Ihews the Abfurdity of the contrary Opinion : And in the 
next LeSlure he removes the Obje&ions alledg'd againft the Diviiibility of 
Quantity } by demonstrating thofe very AfTertions to be true, which the Ob- 
jeftors alledge as abfurd Confluences of the Divifibility of Magnitude in 
Infinitum. 

As Firft, That a finite Quantity may have an infinite Number of Parts. 
For if the Line A B* be divided into an Hundred Parts, all thofe Parts ta-* Plate 3. 
ken together will' be equal to AB; and if it be divided into a ThoufandFig. 3. 
Parts, all thofe Parts taken together will ftill be equal to AB. Now, 
a Thoidand may be encreafed in any Proportion, nay, mtfy receive an 
infinite Addition of Numbers - 0 and fince, however the Number of Parts 
is encreafed, the Sum of them can never exceed the Line AB; the 
faid Line may, without an Abfurdity, be faid to contain an infinite Num- 
ber of Parts. 

Secondly, That it implies no Contradiction, but is agreeable to Geometry ^ to 
fay, that a Finite may be equal to an Infinite -> fhewing that a finite Space is 
equal to an infinite one, and that an infinite Solid is equal to a finite one. 

Thirdly, That there are Infinites, whofe Magnitudes bear certain Propor~ 
tions to one another, and that feme are bigger, (nay infinitely bigger) than 
others. 

In the Circle ABFf take an Arc B F infinitely fmall, then the Chord f Plat** 3. 
B F will be infinitely fmaller than the Diameter A B-, and yet it will be Fig. 4. 
infinitely greater than the vers'd Sine B G, found by drawing F G perpendi- 
cular to B A. Likewile in the Circle BF.A* if the Arc BF be taken* Plate 3* 
infinitely fmall, B E be its Tangent, FG the Right Sine, B G the vers'd Fig. 5* 
Sine, and FH equal and parallel to the vers'd Sine j it is demonstrable, 
that CB is infinitely greater than BE, and BE infinitely greater than B G, 
and B G than HE. 

But the moft furprizing thing of this Kind, is, that if A E and 
A-B f be drawn at right Angles, and the Parabolic Curves of different f Plate. 
kinds, C,D, G, H, be drawn thro' the Point A> the Angle of Contact Fig. 6> 
F A C, which is infinitely left than any rectilinear Angle, will be infi- 
nitely greater than the Angle FAD, and FAG will be infinitely lefs 
than FAD: And fb there may be an infinite Series of Angles of Con- 
tad going on infinitely, of which every following one is infinitely greater 
than the former ; Nay, between any two Angles, there may be inferted 

E innumerable 



26 



A Courfe of Experimental Tbilofophy. 



Annotat. innumerable Angles infinitely greater than each other. And even between 
Left. I. any two of thefe Angles, there may be a Series of intermediate Angles 
v«^*~V"nj going on in Infinitum , of which every, following one is infinitely greater 

than the former. And thus Nature knows no Bounds. See the Demon** 

firatkns of thefe Proportions in the fame Book, Led. 4. 

5 , ] 6 — - There are Atoms, &c] Dr. Keil in his Introdu&ion, LeB. 5 u 
deduces the two following Theorems from the infinite Divisibility of 
Matter. 

T H EO REM I. 

cc Any Quantity of Matter, how fmall Ibever, and any finite Space, how 
u great foever, being given - 0 (as for Example, a Cube circumlcrib'd about 
u the Sphere of Saturn) it is poffible for the Matter of that fmall Sand 
" to be diffus'd throughout all that Space, and to fill it lb, that there Ihall 
u be no Pore or Interfile in it, whofe Diameter ihall exceed a given 
€c Line. 

From the Demonftration of this Theorem, he draws the following Cor oh 
Jary, which ferves for the Demonftration of the other. 

Cor. u Hence there may be given a Body, whofe Matter, if it be re- 
u reduc'd into a Space abfolutely full 3 that Space may be any given Part 
^ of its former Magnitude., 

Theorem 2. 

<c There may be two Bodier of equal Bulk, whofe Quantities of Mat- 
<c ter being unequal in any Prd^ortion } yet the Sum of their Pores, or the 
€< void Spaces in the two Bodies, ihall be almoft equal. 

The Doftor applies his Demonftration to an Inch Cube of Gold, and an 
Inch Cube of Air , the Subftance of which is as follows. 
* Plate 3. The Cubic Inch of Gold, * A contains near 20000 Times more 
Fi £' 7 ' Matter than the Cubic Inch of Air B, but we will only fiippofe 
it to contain 1 0000 Times more. Now let the Matter in A be re- 
duced into a Space abfolutely full, which we will fuppofe equal to the 

- — - — Part of a Cubic Inch 1 (which may be done by the Cor. of the laft 
100 000 

Theorem. Then if the Matter in B be reduced to a Space abfolutely full, 

it will only 'take up the Part of a Cubic Inch, becaufe B 

, 1 000 000 000 

contained 10000 Times lefs Matter than A. To compare thefe two full 
Spaces let us make the Denominators of the two Fractions the fame - 7 

and 



A Courfe of Experimental Philofophy. 27 



an d - — ?£22^_ w i]l exprefs the folid Space in the Inch of Gold : There- rSfT 
i 000 000 000 juecc. 1. 

fore the ■ 999 99—2H remaining Parts of that Cubic Inch will be void 
1 000 000 000 

laces^ whilft the void Spaces in the Inch of Air, (after its Matter has 




been reduced to a folid) are exprefs'd by theFra&ion ■ 999 -^-- 99 1 And 

1 000 000 000 , 



confequently fince the Numbers 999 990 000 and 999 999 999 are almoft 
in the Ratio of Equality) the void Spaces in both Bodies are nearly 
equal. 

Thpugh thefe theorems feem inconfiftent with the Doftrine of Atoms, 
they do not overthrow it } becaufe, as they are deduced from the Divifibi- 
lity of Quantity, they are rather Mathematical than Phyfical. ^ For though 
an Atom may be conceiv'dof an exceeding Smallnefs, yet its Diameter muft 
be of a determinate length, and confequently too big to anfwer the Condi- 
tions of the firft Theorem, which fuppofes no firft Parts. But then even in 
an Atom (or firft Phyfical Part) Mathematicians may affign Parts fmaller 
in any Proportion, fo as to agree with the forementioned "theorems : For 
thofe Particles of natural Bodies, which cannot be divided in the Opera- 
rations of Nature, do virtually contain an infinite Number of Parts - ? tho' 
thole Parts are never feparated from one another. 

Notwithftanding', that giving Atoms a certain Bignefs limits Dr. Keifs 
Theorems in the Phyfical Senfe yet it appears from Phenomena, that there 
a&ually exift Particles finall enough to agree with the firft Theorem, if" a 
Grain of Sand be made ufe of to fill the Sphere of Saturn y and with the 
fecond Theorem, if an Inch of Gold be compared with an Inch of Air ; on- 
ly fuppofing (which is more than probable) that a Body perfeftly folid is 
as much denier than Gold, as Gold is denfer than Light, or ^Ether which 
is ftill rarer than Light. 

And if a Grain of Sand be fuppos'd divided into fo many Parts, as to 
fill the Sphere of Saturn, without having any Pore bigger in Diameter than 
an Hair ; thofe Particles may be ftill bigger than thofe of ^Ether, if not 
bigger than thofe of Light 

[7- — Thefe are to be imaged of an unconceivable Smallnefs, &c.] 
Though it be furprizing to think, that Matter fhould be aaually divided 
into Parts fo finall, as we have mentioned in the foregoing Note j a few 
Inftances of the finall Parts into which it is divided by Art, or the Work of 
Mens Hands; and fome Examples of its Subtility, as it is naturally difpers d 
all over the Univerfe, will make the Affertion very plain to any Body that 
will afford the leaft Attention. . 

The Gold-Beaters, even with courfe Tools, reduce that Metal to iuch a 
Thinnefs, thatfifty fquare Inches of Leaf-Gold" weigh-but one Grain. Now 
the Length of an Inch may be divided into 200 vifible Parts, as appears in 

E z 1 late 



2 8 A Courfe of Experimental Fhihfophy. 

Annotate Plate 3. Fig. 8. where the ?cth Part of an Inch is diftinguifli'd Into ten 
Left. L vifible Parts by fix black Strokes and five white Interftices # * Then multi- 
O^/'NJ plying 200 by 200 we have 40000., for the vifible Parts of a fquarelnch} 
* Plate 3. which are contained 50 Times in a Grain of Gold - } and therefore by this 
Fig. 8. * Means it_ becomes divided into 2 000 000 of vifible Parts. 

If we confider the gilding of Silver, we fliall find Gold in that cale to 
con ain vifible Parts, even after it has been divided above ten times more y 
for eight Grains of Gold will gild a whole Ounce of Silver, which is after- 
wards drawn into a Wire i 3 000 Foot long j therefore one Grain gilds a Wire 
16 2 s Foot long - 7 and as every Foot ( by what we have faid above) muft 
contain 2400 vifible Parts, the whole Length of the Wire contains 3 900000 
little Cylinders, which being turn'd into Cubes, will each of them have 
fix vifible Sides - 0 and conlequently by this laft Operation, one Grain of 
Gold, inftead of being divided into Two Millions of vifible Parts, will 
be divided into 23 400 00c, which is almoft twelve times as many, 
fThat one may reafonably take Cubes for the little Cylinders , appears, 
when we confider further, that all this Wire is beaten flat in order 
to wrap it round Silk for making Gold Lace 5 and that even after flatten- 
ing, the beft Mifcrofcope cannot dif cover the Silver through the gilding. 
This fliews, that in this thin Skin, feveral Parts of the Gold ftill 
lie upon one another - 0 though the Thicknefs of it ( as Dr. Bailey 

haslhewn, Philof.7ranfaff. l$umh. ip^.) is but — - — Part of an Inch, or 

12450 

622 i times lets than the 200th Part, of an Inch that we have taken, as 
the leaft vifible Part of an Inch in Length. 

Mr. Boyle, in his. Book of "The Nature and Subtilty of Effluvia, mentions,, 
that one Grain of Copper diffolv'd in Spirit of Sal Armoniac, will give a 
ftrong blue Tinffcure to 105,157 Cubic Inches, or near two Quarts of 
Water. Now iuppofing no lefi a Cube of this ting'd Water to be vifi- 
ble, than ftch a one whofe Side is equal to the iooth Part of an Inch 
(which is making eight times more Allowance than we did in relpe£t 
of the Gold) it will appear upon Computation, that a Grain of Sand €0 
Imall, that a Million of them may be contained in a Cubic Inch, does con- 
tain two Millions an Hundred and eleven Thoufand and four Hundred (or 
n in 4oo)luch Parts as the fingle Grain of Copper isa&ually divided into. 

The lame Gentleman, having exposed to the open Air a certain Quantity 
of Afa Ftetida, found it diminifh'd in Weight but the eighth Part of a 
Grain in fix Days. Now if we fuppole, that during all that time a Man 
could fmell the AJfa Ftetida at the Diftance of five Feet, it will appear, 
that the Particles^ into which th§ Afla Fcetida is divided, cannot exceed in 

Bignefs the ~— i — _ Part of an Inch. 

20 250 000 000 000 000 

The late Mr.Lewenhoek, that ingenious Searcher into Nature,gives us an Ac- 
count, that in the Milt of one Cod-Fifli there were more little Animals, than 
there are Inhabitants upon the Face of the Earth. Now by only knowing 

the 




the Focal Length of the Letts, or Glafs of the Microfcope, we can by the Rules Annotat. 
of Optics 'find the bignels ofthofkJnimalcula, which cannot be To big as the Left. L 

_J , — -Part of a Cubic Inch: And, therefore, feveral Thou*- 

%6 ooo ooo ooo ooo 7 7 

fends of them might ftand upon a Needle's Point. And it appears'alfo, that 
if we compare thefe to a Whale } they will be much lefs in Proportion^ 
than a Whale is, when compared with the whole Globe of the Earth.' 
As every Animal is an organized Body ; how fine, delicate and fubtilemuffe 
be the Parts that make up one of thefe Animals ? How fmall muft be its 
Heart ? How inconceiveably little its Veins and Arteries ? And much lefs 
muft be the Globules of that Fluid which ferves it for Blood, and 
which are ftill carried along in a finer Fluid.— It is worth while to confider 
the Smallnefs of thofe Globules j which we may do by making the follow- 
ing Allowance; namely, That the Particles of Blood, of thofe Animals 
are as much lefs than their Bodies, as the. globular: Particles of the hu? 
man Blood are lefs than a Man's Body. 

A Man's Body is to that of an Animalculum y as 17 to — ^ — and the- 

~ 100 000 

Diameter of the Globules of a Man's Blood are not bigger than — — - 

79 200 

P&rt of an Inch f , (becaufe Lewenhoek found the Diameter of the VeflelS 

through which they run to be no bigger) therefore as 17 is to ^— ,io 

100 000 

is - — - — to ~ — or in Decimals — ^ — — 3 there- 

79 200 134 040 000 000 1 000 000 000 000 

fore the Globules of Blood in thefe little Creatures cannot be fo big as the 

8 

Cube of this Number or — — = — — — — — — 

1 000 000 000 000 000 000 000 000 000 000 000 

Parts of an Inch. 

But fmce thefe Numbers, exprefs'd in Figures, do not immediately 
give an Idea of the Smallnefs of thefe Globules Dr. Keil (in whole Fifth 
Letture one may find at full Length the Demonftrations, that prove our 
two laft Paragraphs ) has fiaewn, that the fmalleft vifible Grain of Sand 
would contain more of thefe Globules,, than ten Thoufand two Hundred and 
F'ifty-fix of the higheft Mountains in the World would contain Grains of Sand. 

What we have laid hitherto, iliews into how many fmall Parts Bodies are 
actually divided } but there are Particles of Matter, fo much fmaller than 
the Globules abovementioned,, that thofe Globules compared with them 
will not only be as Mountains, but as vaft Earths. I mean the Particles 

■f Tbe learned and ingenious Dr: J. Juria, Seer, of the Royal Society^, has not long fince found 
Globules of the human Bhcd to be bigger than what is here mentioned; and haviw communi- 
cated his Obfervationstd Mr. Lewenhoek 3 was by him confirm* din his Ajfertion ; but J^drd not think 
proper to, alter this Calculation^ dncc ' / $ah !fyeak fully upmthis 'Subfeft in another Place, of 'WisCourfe. 

at. 




3° 

Annotat of Light, whofe inconceivable Finenefs puzzles cur Conception. How 
Lett ' I. amazingly little muft thofe Particles be which flow from fuch a Candle, 
whofe Light may be feen at two Miles Diftance ? Since every Inftant of 
Time, Particles muft be darted out to fill a Sphere of four Miles in Diame- 
ter, fo that a Pin's Head cannot be placed any where in that Sphere with- 
out receiving fome Particles of Light. Dr. Newentiit Ihews, that the 
fourteenth Part of a Grain of Wax or Tallow, (that is confirmed in one 
Second of Time in a Candle of fix to the Pound,) produces a greater Number 
of Particles of Light, than a Thoufand Times * a Thouland Millions of 
Earths, (equal to our Earth) would be able to contain Grains of Sand. See 
Religious Philofopher^ Vol. 3. Contemplation 25. SeSt 7 15, 1 <5, 17. 

7. [y—7^here mujl be a great deal of Vacuity r , &c] The different Ipe- 
cifick Gravity of Bodies plainly proves this Affertion, as will be more ful- 
ly Ihewn in the fecond Le&ure. And in Fluids this is evident from their 
different Refiftance, which we have already Ihewn to be proportionable to 
the .Quantity of Matter in Bodies. 

8. [ All Spaces are not equally full of Matter,"] If there was any 

fuch thing as a Subtile Matter , that wholly fill'd up the Vacuities of Bodies, 
and the whole ^Ethereal Space in which the Planets move:, its Refiftance 
would be fuch as far to exceed the Refiftance of Quickfilver. In fuch a 
Medium as that, even a perfe&ly folid Globe muft lole half its Motion, 
before it could move thrice the length of its own Diameter - 0 andrluch 
Globes, as the Planets are, would be ftopt much lboner } wherefore 'tis ab- 
folutely neceffary for continuing the Motions of the Planets and Comets, 
chat the Places, they move in, be almoft entirely void of Matter. That 
they are fo, appears from the Iwift Motion of the Tail of a Comet, 
that does not appear to meet with any lenfible Refiftance in the Medium 
in which it moves, though it is expanded fo wide, and made up of lb thin 
a Vapour. 

9. [9 Much more Vacuum than Matter^ &c] That there is more 

Vacuity in Bodies than Matter, may be clearly deduced from the Proper- 
ties of tranlparent Bodies ^ for the Rays of Light are ipread every way in 
right Lines through Water, Glafs, or a Diamond, with no more Difficulty 
(nay, with more Swiftnefs) than they are carried through the Air, whatfoever 
Side of the tranlparent Body be expoled to the Light*, therefore there is 
always a reftilinear Palfage for the Light, from the leaft affignable Part of 
the tranlparent Body to any other Part of it : And this could never happen, 
imlefe the Quantity of Matter in fuch a Body was extremely Imall when 
compared with its Bulk. Perhaps in a Diamond the folid Matter, compared 
to its Bulk, bears a lefs Proportion than the Diamond does to the whole 
Cilobe of the Earth : Which will not appear impoffible, to thole that confi- 
4er what has been laid before upon this Subject. Now fince Gold is not 

above 



A Gourfe of Experimental q i 

above fix times denier than a- Diamond, how much more Vacuity muft be Anno tat. 
in it than Matter ? This fhews the Reafon why the Effluvia of the Load- Left. I. 
ftone pafs through Gold as eafily, as through the Air ^ for if a Plate of Gold, ' 
or any other Metal (except Iron) be interpofed between a Loadftone and a 
touched Needle, which is drawn out of its Pofition by the Virtue of the 
Stone, the Needle will in no wile be lefs affe&ed than before. Nay thofe 
Effluvia may for a whole Day pafs through the Brain, a Body fo tender 
and of fo delicate a Contexture, without affe&ing the Nerves with any 
Senfation, or difturbing the leaft Thought. 

The Vapour of the Aurora Boreqlis (which fome imagine to confift in a 
great Mealure of the Magnetic Effluvia of the Earth ) does ri'eely pais 
through Houfes and Trees, and dart through the Bodies of Animals without 
being felt ; as appears from Obfervations made upon that Phoenomenon 7 when 
viewed from leveral Places at once. 

10. [15. Any Weight may hang, &c. The lame Experiment may be 

made, by Means of a Ipiral Spring in one of the Balls within a Barrel on 
which a String is wound up. For the end of the String being faften'd to ano- 
ther Ball equal to (or double, or triple) the Ball that has the Spring upon 
pulling the Balls afunder, they will come together again with Velocities reci- 
procally proportional to their Mafles. See Plate 3 . Fig. 9. Where A *repre- * Plate % 
fents theSedion of an hollow Brafs Ball, with a fpiral Spring S and Barrel Fig. 9, 
within it, contrived in luch Manner as to pull back into the Ball the whole 
String A B, when it has been pulFd out by the End B. The Ball B is fo- 

lid and of Ivory, but of the lame Weight as the hollow Ball A. Now if 
the Ball B be pulled from A to the Diftance A B, upon letting go both 
the Balls at once, they will meet at C, the middle Point between them - 0 but 
if B be a Ball twice as heavy as A, upon letting both go they will meet at 
D, D B being but half of the Diftance A D. 

11. [ 1 7' For Gravity being a Virtue diffused, &c] When we compare 

Gravity to Light and Heat, we would not be underftood to derive their 
Effects from the fame Caufe - 7 or to affert, that all Sorts of Attractions in 

Bodies have the fame Laws, lincethe Attra&ion of Cohefion*, and the At-* L - X -N°.ift 
traftion of the Loadftone f , do not aft in that Manner : But here we only 209 &c ' 
Ipeakof the Attraftion of Gravity, whereby the Bodies about us are driven^ L * X ' N ° ,:2 ^ 
towards the Earth, and the Earth and Planets are driven towards the 
Sun \ which Attraction is called alfo a Centripetal Force: And whatever be 
its Caufe, its Laws abovementioned have been dilcover'd by Obfervations 
and Experiments, which have always concurred to confirm the Theory of 
Gravity. 

In order to have a clear Notion of the Eflfe£ts of Gravity, or the Centri- 
petal Force, we muft confider it in three Refpefts : Either in refpe£t to the Quan- 
tity of Force in the Central Body that attrafts others, (or towards which Cir- 
cumambient Bodies tend) which is call'd the Abfohte Force ^ or in refpeft 

to 



2 A Comfe of Experimentd Phih/bfby. 



Annofcat. to the Telocity with which other Bodies move towards the Central one, which 
Left. I. is call'd the Accelerating Force or in relpeft to the Quantity of Motion in 
s*s~\r*s^ the laid Bodies, when compared with each other, which is proportional 
to the Obftacle that they are able .to remove, and is called the Moving 

Force. 

The Abfolute Force is proportionable to the Efficacy of the Caiife that 
fpreads its Virtue from -a -Center round about. So if the Earth had twice 
the Quantity of Matter that it has now, (whether it was twice as big, or 
only twice as denfe) it would have twice the Abfolute Force. Thus the 
Moon has near forty times lefs Abfolute Force than the Earth, becaufe it 
has almoft forty times left Matter. Its Bulk indeed, (which is as the Cube 
of- the Diameter) is almoft fifty times left than that of the Earth} but 
then it is denfer in the Proportion of 21 to 17. See Sir Ifaac Newtotfs 
Prtncipa, Book. 3. Prop. .37. Corol 3. 

The Accelerating Force is exprefled by that Velocity generated in a given 
Time, with which Bodies (confidered as Phyfical Points) move towards 
the cetitntl Body attracting them by its Abfolute Force. And this Accele- 
rating Force is greater or lefs according to the Diftance of the Center of 
'* Left* 1. the Force, in the reciprocal duplicate Proportion abovementioned.* Thus 
M°. t?j. j S t ] ie Gravity, that makes Bodies tend towards the Center of the Earth, 
greater in Tallies than on the Tops of high Mountains; greater at the 
Poles than at the ^Equator, which is feventeen Miles higher ; and greater 
at the Equator than at greater Diftances from the Globe of the Earth: For 
the fame 'Body, which, near the Surface of the Earth, falls fixteen Foot 
.in £he;firft Second of its Fall, would fall but four Foot in the fame time, if 
it began to fall at the Height of 4000 Miles from the Surface of the Earth, 
or two Semidiameters Diftance from its Center. At <£qual Diftances the 
If Left. 1. Accelerating Force is the lame every where: becaufe att Bodies large or 
No, 8. Ex- jfo ia ll, heavier or lighter, (abftrafting from the Refiftanceof the Air,) are 
¥ per. i. equally accelerated in their Fall."} - . 

The Moving Force is proportional to the Quantity of Motion, which 
the Abfolute Force of the central Body generates in a given Time, in the 
Bodies that it afts upon. Though in relpeft of the Earth, we confider the 
bigg^ft Bodies that are attracted by it (and even the Moon it felf ) as Phy- 
fical Points } yet when we compare the Bodies with each other, we muft 
have a Regard to their refpe&ive Quantities of Matter ^ for Bodies that 
have the fame Accelerating Force, or move with the fame Velocity, have* 
their Quantities of Motion greater or lefs, as they have more or lefs Mat- 
ter, or as they are more or lefs heavy becaufe the Moving Force of a 
Body is made up of the Sum of the Aftions of the Accelerating Force of 
all its Parts, and confequently it is found by multiplying the Quantity of 
Matter into the Accelerating Force j as the Quantity of Motion in Bo- 
dies is founds by multiplying their Matter, or their Ma% into their 
Velocity. 



Hence 



A Courf ? of Experimental PBhfophy* g g 

^ Hence near the Surface of the Earth, where the Gravitating or Accelera- Annotat 
ttng Force on all Bodies is the lame, the Moving Force or Weight is as the Led I * 
Body : But if we afcend to Places where the Accelerating Gravity is lefs 
the. Weight will alfo be diminiih'd and become as the Mafs of the Body 
multiplied by the Accelerating Force. Thus if a Weight of one Pound and 
a Weight of four Pounds begin to fall near the Surface of the Earth, 
their Moving Forces will be as 4 and 1 ; for if we take 16 for the Accelerating 
Force, equal in (and common to) both, 1 6 times 4, (or <5 4 ) will be juft 4 times 
-as much as 1 6 y (or 1 6 times 1 .) But if the four Pound Weight was remov'd 
to the Height of 4000 Miles, or two Semidiameters from the Center of the 
Earth, its Moving Force then would be juft equal to that of one Pound at 
the Surface of the Earth - 7 becaufe the Accelerating Force being 4 times lefs 
at.twice the Diftance from the Center, 4 times 4 or 16 would then exprefs 
the Moving Force of the heavier Body, 

If the one Pound Weight was plac'd at the Diftance of two Semidiame- 
ters, its Moving Force would be 16 times lefs than that of the 4 Pound 
Weight at the Surface of the Earth. 

A clear Idea of thefe three Forces will ftiew the Reafon of fowc Pheno- 
mena y which would otherwife be hard to explain : As for Example, we 
have already faid, that the Earth has near forty times more Matter than the 
Moon 5 and yet Bodies on the Surface of the Moon weigh, but three times 
lefs than they do on the Surface of the Earth,though the Moon's Abfolute Force 
be forty times lefs. But to fhew that this is a neceffary Confequence of 
what has been faid, let us examine this Matter by Numbers. 

Let *T A B reprefent the Earth, and L the Moon, A B a Diameter* pi ate ^ 
of the Earth, and b d a Diameter of the Moon (which are to one another Fig, 10. * 
as the Numbers 365 and 100) and let the Lines CE and ce be each equal 
to a Diameter of the Earth. Now if we fuppofe a Body plac'd at E, 
whofe Weight or Gravity towards the Earth is there equal to 9,8 . 2 7 Pounds ; 
the fame Body piac'd at <?, juft as far from the Center of the Moon, as it 
was before from the Center of the Earth, will weigh towards the Moon L 
but 0,25 Pound, or aQuarter of a Pound becaufe the Maffes or Quantities of 
Matter in thole two Bodies, and con fequently their Abfolute Forces, are to 
one another as thefe Numbers, or as 39,721 to i, which are in the fame 
Proportion. Newtoni Prin. Lib. 3. Prop. ij.Cofoi.4. 

Then if the Body abovemention'd be piac'd at A, diftant from the Center 
of the Earth but a Semidiameter, it will f weigh towards the Earth four xl u ^ 0 r , 
times more than it did at E or 39,721 lib, and at a it will weigh towards 
the Moon 1 lib. or 4 times more than it did before, for the fame Reafon. 
Now if the Moon, without any new Addition of Matter, was fo expanded or 
rarified, as to fill up the Sphere ma 9 which is equal to the Globe of the 
Earth, then the Point a would be on the Surface of the Moon, as the 
Point A is on the Surface of the Earth and in that Cafe the 
Weight of Bodies on the Surface of the Earth would be to the Weight 
of Bodies on the Surface of the Moon, pretifely as the Quantity of Matter 
in the Earth, to the Quantity of Matter in the Moon and conf equently as 

F their 



A Courfe of \ Experiment al PhiJofophy. 

Annotat, their Abfolute Forces. But as the Moon, is lefs in Diameter than the Earthy 
Left.' I. when the Body that weighed i lib. at a comes to be placed on its Surface 
LXVXJ at d 9 it will be nearer to the Center of the Moon than it was, in the Pro- 
•* x >j 0 portion of 182, > to 50, or 365 to . 100, and therefore * it will then weigh 
1JeW * 81 13^225 lib ^ for as the Square of c d (100X100=10000) is to the Square 
oi c a (365X^5=153225) fo is 1 , or the Weight of the Body placed at a, 
to 13,? 225, the Weight of the fame Body upon the Surface of the Moon j 
which Number being very near the third Part of 3.9,3 7 r , ihews, that Bodies 
on the Surface of the Moon weigh about a third Part of what they do on 
the Surface of the Earth. Which was to be demonfirated. 

Hence it follows, That Bodies weigh more on the Surface of the fmall 
Planets, in Proportion to their Quantity of Matter, than on the Surface 
of the larger. Thus upon, the vaft Globe of Jupiter, whofe Quantity of 
Matter or Ahfolute Force is 2 20 times greater than that of the Earth, Bo- 
dies weigh but twice as much as they would do upon the Surface of the 
Earth. And upon the immenfe Body of the Sun, whofe Quantity of Mat- 
ter is 227512 times more than that of the Earth, Bodies weigh only 24,4. 
times more than they do upon the Surface of the Earth, 

Hence follows alfo, that in refpeft of any Planet or central Body, as for 
Example, the Earth, the Weight of Bodies gravitating towards its Center 
is greater on its Surface, than at any Diftance without it, or any where 
within it, though nearer the Center. For if the fame Body which at A 
weighed 39*371 lib. foould be brought to D a Point within the Earth as 
near to C the Center of the Earth TAB, as d is to c the Center of the 
Moon L, it would not encreafe its Weight towards C 13,3225 times, as it 
does when remov'd from a to d % but it would diminifli it in the Propor- 
tion of 365 to ioo, becaufe that Part of the Earth towards the Surface be- 
tween D and A attracts back the Body towards A. 

The juft Proportion of this Decreafe of Gravity is determined by Sir Ifaac 
Newton, Lib. .3. Prop. 9. to be always as the Diftance from the Center^ 
going from the Surface downwards : And as the Principles from which it is 
deduced are very evident, I fliall repeat them here. 

If there be a concave fpherical Surface, whofe Particles attract accord* 
<§• Plate 3. i n g to the Laws of Gravity abovementioned, as XHKL,f a^y little Bo- 
■K& 11* <}y within it will remain at reft where ever it is plac'd, the Attraftions 
round about deftroying one another. This is evident, if the Body be 
placed at C in the Center. And if the Body be plac'd at P as near again 
to H I as to KL, the fame thing will follow \ for let the Lines I K and 
KL, be drawn* and it will be evident that the fpherical Segment be tweent 
K and L will be four times greater than the Segment between I and 
becaufe K L is equal to twice H 1^ therefore there are four times more at- 
trafting Particles at K L than at H I, but H I being twice nearer to the 
Body P attra&s it four times as much, which makes amends for the fewer 
Particles contained in the leffer Segment 5 for the Product of the Abfolute 
Force, of. HI (1) multiplied into its Accelerating Force (which here is 4) is 

equal 




A Courfe of Experimental rhilofophy. 35 



equal to the Product of the Abfolute Force of K L (4) multiplied into its Annotate 
Accelerating Force, which is but 1. tfhis will hold good in refpeff of. any other 'Left:.. I. 
Part of the Surface or Pofition of the Corpufcle : And if the Corpufcle be put \^*~V"n- 
into Motion, it will go on uniformly in the concave Sphere y as if it was not 
an ratted at all If inftead of a Surface there was a Shell of any Thick- . 
nefs A BHIKL\ every thing elfe would remain as before afTerted,^ 1 ^^. 
provided that Shell was every where of the fame Thicknefs and Denfity. s ' 

If the Hollow HIKL be fill'd with a fblid Sphere and the Corpufcle 
be plac'd at'P, it will be attracted towards the Center C only by the 
Force of the inner Sphere H I K L - 0 for the attra&ive Forces of the feve- 
ral Parts of the Shell deftroy one another, as has been fhewn before. If 
the Corpufcle be remov'd to CL, it will be only attracted by the Sphere 
QR. Let us fuppofe the Abfolute Force of the whole Sphere A B — 64 ; 
the -Lines B C> P C, and QjC, as 4," 2, and 1 5 and the Accelerating Force 
of the Corpufcle at B to berri - 7 its Moving Force will of confequence be' 
64. Now if the Corpufcle be brought to P (as near again .to the Center 
of the Forces) its Accelerating Force will be 4, but then that Number 
mull: only be multiplied by the Abfolute Force of the Sphere H IK L, which 
being twice lefs in Diameter than the Sphere AB is eight times lefs in Soli- 
dity, and therefore its Abfolute Force will be but 8j which multiplied 
into the Accelerating Force 4, gives only 32 for the Moving Force of the 
Corpufcle at P. If the Corpufcle be brought to Q, four times nearer to 
C, its Accelerating Force will be 16 5 which being multiplied by 1, the Ab- 
folute Force of the Sphere Q_(which is four times lefs in Diameter than the 
Sphere AB) will give 16 for the Moving Force of the Particle at Q. 
Now fince the Moving Forces, whereby the Corpufcle or Particle at B,P, 
and Q_ gravitates towards the Center C, are as 6q 9 32, and 16, and the 
Distances from the Center are as 4,2, and 15 it follows, "Hh at going from the 
Surface of a Planet downwards, the Gravity decreafes difeSily as the Diftancg 
from the Center. Which was to be demonftrated. 

To apply this to what w r e faid before :» if we conceive a Globe C D 
within the Earth T f eqijal to, and equally denfe with the Moon : The \ plate 3 
Body which at A weighed 39,721 lib. will at D weigh juft 13,3225 Pounds, Kg- 10 
as it would do upon the Moon's Surface. 

12. [18— if a Cube of an Inch, &c] As in the Bodies fhin'd upon 
we only confider the Surfaces enlighten'd:, the Experiment may be made with 
iimilar Pieces of Paftboard expofed to the Light : As for Example, a Cir- 
cle, a Square, a Pentagon, or any other Polygon of an Inch Diameter a Foot 
diftant from the Candle, will receive the fame Quantity of Light thatJalls 
upon a Circle, Square, or Pentagon, &c. of two Inches Diameter at two 
Foot from the Candle, or the like Figures of three Inches Diameter at 
three Foot from the Candle; where' we are to obferve, that the Strength of 
the Light is diminifh'd in the lame Proportion, as the Area of the Fi- 
gures is encreafed j That is ? here at the Diftances of i 9 2, and 3 Feet, the 

F 2 Strength 



A Courfe of Experimental Phi, 




Armotat. Strength of the Light will be as 9 > 4, i 5 which we call a reciprocal Du- 
Le&. I. plicate Proportion of the Diftances. 

13. [19— When the Wood is more f olid, &c] If we make xAe of a Glue 
whofe Parts are finer in Proportion to thofe of the Wood to be joined to- 
gether, it will hold as faftas infofter Wood - 0 as is experienced, when hard 
Wood is glued with Fiih-Glue diffolv'd in Spiritof Wine. 

14. [ip—Fhe Figure of any Portion of a Fluid, &c] When two fmall 
Drops come to touch one another, they firft become oval, and then im- 
mediately ipherical. Now when the Drop is of an oval Figure, the Pref- 
ftre of an external Fluid afting upon it from all Parts cannot alter the Fi- 
gure of the Drop fo as to bring it to be round ; neither can it make it flat- 
ter, as fome have imagin'd, who have afTerted, That if there was no 

Attraaion of the Particles of the Liquor, but only the PrefTure of an exter- 
nal Fluid, an oval Drop would be more prefs'd againft the Ends of the 
fhort Diameters, than againft the Ends of the long one, or of the Drop, 
which would caufe it to be lengthen'd. But I fhall not make ufe of this 
Argument, becaufe it is a Fallacy as will appear to fuch as will be at 
the Pains to conmltSir If. Newton's Prineipia Lib. 2. Prop. i 9 . where it is 
demonstrated, that if any Portion of a Fluid be preffed by the fame or 
any other homogeneous Fluid afting from all Sides, that Portion will not 
have its Figure alter'd by that Preflure, 

if* [19— Whereas; from a mutual ' Jtlrafflon of the little Globules, Sec. 1 

* Hate 2, If two fimilar and equal Globules A and B * attract one another and touch 

J 3- at G, they will remain at reft, as they would if they touch'd at E or at D, 
or any other Point in the Circumference of either of them, becaufe the. 
Contaft would ftill be the fame : And therefore a very fmall Force wilt re- 
move B from its Contact at C to E, or any other Point of the Circumfe- 
rence ( or rather of the Surface of the Sphere ) C E D ; becaufe in going 
round one Globule it ftill continues to touch it as much as it did before. 

* Plates/ If there be three Globules A, B, F, ftouching one another in fuch man- 
Ixg. 14. ner , that their Centers are in the Line a b, they will remain in that Pof> 

* Fig. 15. tion r but if any one of them be mov'd out of that Pofition as F*, it will 

not remain at F, but move on toward C where the other Globule A 
will meet it, fothat each of the three Globules will touch in two Points, 
being as many Points as three Spheres can touch one another in, See 




<$'F»g, 17. If there be four Globules in the Pofition g A, B,/, they will for the 
fame Reafons come into the Pofition A,F, B, G, fuppofing their Centers all 
in the fame Plane y but if any one of them, as F, be lifted up, it will not 
reft till it comes to c, and then the Spherules will toucheach of them in 
three Points. Hence it is, that when two Drops of Water r or any other 
liquor coming to towk one another, make up the Spheroid ac dbef t 

they 



A Courfe of Experimental Thilofophy. 37 

they will not preferve that Figure, but run into the Sphere c g d e h /, Annotat. 
that there may be the greateft Contact poffible between the Globules of Left. I. 
which theSphere or new Drop is made up. WVn 

Now becaufe it may be thought unmathematical to draw Confequences 
from the Figure of the Parts of Fluids, without having firft demonftrated 
that they are fpherical 3 I fliall here fubjoin another Proof of the Round- 
nefs of the Drops of Liquors, without having any regard to. the. Figure of 
the Particles of which they are compounded, 

Let^ ABDE be a Portion of an homogeneous Fluid whofe Parts at-* Plate 3^ 
raft one another, and whole Figure is not Ipherical. If in luch a Fluid Fi & ■ ^ 
we fuppoie a Syphon as ACE ( or which is the fame thing, if all the 
Fluid fliould be frozen, except the Canal A C E) whofe Legs A C and C E 
are unequal, and meet at C the Center of the Fluid, towards which there 
is the greateft Attraction ^ the Fluid will run out at A in the Leg A. C y 
till it be come down as far as g in the Leg C E, fuppofing Cg equal ta: 
A C. But if the Leg A C be lengthened as far as c 9 then the Fluid will- 
only come down as far as e in the Leg C E, and at the fame Time rife up* 
to a in the Leg C a, C a being equal to C e. 

If fuck another Canab or Syphon be fuppofed at BCD, the Fluid in it 
will come down from © to ^ and rife from B to b. And fince luch Si- 
phons may be fuppofed all over the Fluid A B D E, that Fluid "by the. 
Attraction of its Parts mull needs be reduced to the Ipherical Figure ab de v 
Which was to he 'demonftrated^ 

id* [20 — -Having moiftened. Sec. two G!afs-PIanes y &c.J This Expe* 
riment of the Drop of the Oil of Oranges, having been made by the late' 
Mr, Hauksbee^ in the Manner that; Sir Ifaac Newton relates it in the 
third. Part ofhisOptics {Query the laft 7 towards the Middle) that incom- 
parable Philolbplier has calculated the Force of the Attra&ion, and lays 5 
u ' That where the Oil of Oranges, between the two Glafs-Planes, is of the 
<c Thicknefs of three Eighths of the ten Hundred Thoufandth Part of am* 
u Inch, the Attraction (collected by the Rule given in the Table of the 
u Second Part of the Second Book) feems to be fo flrong, as within a Cir- 
* c cle of an Inch in Diameter, to fuffice to hold up a Weight equal to that 
* of a Cylinder of Water of an Inek in Diameter^ and two or three Fur— 
f longs in length. 



17. 
nearer. 
Glafs-Planes. 



2o ~-*1fhe jittraSlion muft encreafe^ .continually as the Planes corn® 
There are fix Properties to be obferv'd in the Attraction of thefe 



Let f the Point O (the Center of theDrop) be at equal Diftances firom^ Hat*- 3 
the Glafs Planes Q^, j and let the Radius O b exprefs the greateft Di- Fig, 20, 
fiance at which the Places of Qlafs . Qjn t Q^m can, Jaave any EffeCttrpon the: 
wPoint O* It is plain ? _ 



m A (Jour e or nxpenmen 







Annotat Firfi, That at its greateft Diftance from the Point QL, there will be no 
JLeCt L greater a Part of the Plate of Glafs, than a Circle whofe Diameter is cd 
within the Sphere of Attraction, or whole Parts are able to attraCt the 
Point O, all the other Particles being at too great a Diftance. Secondly, The, 
Force of the Attraction of the Points of the Circle of Glafs which are 
neareft to the Point QJs alio the greateft. 'Thirdly, The Sum of the at- 
tracting Particles plac'd towards and which are contained in the Seg- 
ment of the Circle of Glafs, whole Arc has f c for its verfe Sine, is grea- 
ter than that of the attracting Particles contained in the oppofite Segment, 
In the lame Proportion as the firft Segment exceeds the other, becaufe of 
the Angle made by the Planes at Fourthly, The Direction of the At- 
traction of the Points, that are at the lame Diftance from O, making all along 
the Line Q^R an Angle atO, more acute towards Qthan towards R, the 
Point O will advance towards Q_ with an accelerated Velocity. Fifthly, As 
the laid Point O advances towards Q^, the Diameter of the Circle of Glafs 
whofe Particles can attraCt the Point O will be encreafed, (as g d is greater 
than c d) and eonfequently the Circle alio;; which will caule the Drop of Gil 
to Ipread more and more upon the Planes of Glafs, between which it was 
plac'd. Sixthly, The Drop or Point O will advance towards Q_-, with a 
Velocity always accelerated with greater Forces } becaufe the Angle g O h be- 
comes always more acute in relpeCt to the Angle d O q in proportion as 
the Chord g d becomes greater than the Chord cd, which makes the Bale 
g £ always lefsin refpeCt of the Bafe d q, whilft the Sides of the two Trian- 
gles always remain equal ; and confequently 'the Angle g O h, is always lefs in 
proportion to the Angle d O g\ which continually encreales the Force of At- 
traction towards Q_ by the following Demonstration. 
* BSate 3. Let the * Angle abc be divided into equal Parts by the right Line bu» 
1%. 21, and about the Centers u, taken at plealiire upon that Line, draw the equal 
Circles ghki, acini; I fay that if through the Points of InterfeCtion^ 
the Chords ac,l m\ gh, ik, be drawn the Ratio of Im to a c will be grea- 
ter than that of ik tog h. From the Point b draw the Tangents b ff,brq% 
and from the Poifit u for a Center draw between the faid Tangents the 
Circle eond, and pine d, no. , . 

The Segments de, gh, are fimilar, as well as no^ik, as alio are the Arcs 
fP e 7 & fh-> -which makes 0 0 :: g A : de, and ik\gh% \ no%de. Now Im 
is greater than n 0, and on the contrary a c is lels than d e - 7 therefore 
the Ratio of I m to a c is greater than that of ikto gh: Which proves the 
iixth Property of the two Glafs Planes that touch at one- End, and are 
open'd to a fmall Angle at the other. 

18. [23- — lie Reafon of thefe Phenomena, &c] Dr. James Jurin, Se- 
cretary of the Royal Society, has made a great many curious Experiments 
of this kind, of which he gives an Account in Phil. Tranf. Numb. -355. 
where he ihews in what manner the Attraction of Cohelion operates to raife 
and fuftain Water in fmall Tubes^ and fuch Spaces between foiid Bodies as 
are' analogous to fmall Tubes^ 1^ 



3 




i p« Quickfilver attracts Quickfilver more than Glafs attraBs it, &c] Annotate 

Some have been apt to imagine that Quickfilver and Glafs repel one another, Le£t. L 
becaufe it does not in thele and feveral other Experiments appear to flick l/YM 
to Glals but that it is really attracted by Glals (though lb much lefs than 
by it felf, as to make it feem to be repell'd) will be ftiewn by giving "an Ac- 
count here of feme more Experiments relating to the Attra&ionof Cohefion, 
which the abovementioned ingenious and learned Gentleman made with Glafs 
and Quickfilver* 

Experiment i. 

Quickfilver is attrafted by Glafs. 

If a finall Globule of-Duickfilver be laid upon a clean Paper, and be 
touched with a Piece of cfpan Glals 5 upon drawing the Glafs gently away,, 
the Quickfilver will adhere to it, and be drawn away with it. And if the 
Glafs be lifted up from the Paper, the Quickfilver will be taken up by it, it* 
the fame manner as a Piece of Iron is drawn by the Loadftone, and will ftick 
to the Gkfs by a plane Surface of a confiderable Breadth, in Proportion ta 
the Bulk of the Drop, as manifeftly appears by an ordinary Microfcope* 
Then if the Glafs be held a little obliquely, the Drop of Mercury will roll 
flowly upon its Axis along the under Side of the Glafs till it comes to the 
End, when it will be lulpended as before, 

Experiment. 2. 

If a pretty large Drop of Mercury be laid upon a Paper, and two Pieces 
of Glafs held edge- wile be made to touch it, one on each fide } upon draw- 
ing the Glaffes gently from each other, the Drop of Mercury will adhere 
to them both, and will vifibly be drawn from a globular to an oval Shape \ 
the longer Axis palling through the middle of thofe Surfaces, in which the 
the Drop touches the Glafles. 

*fhe Particles of Quickfilver are more attracted by one another than by Glafs*. 
For the Proof of this fee Lett I. N°. 24*25* 2<5 ? and thofe other Experi- 
ments of Dr. Jurin. ^ 

Experiment 3: Plate 3. Fig, 22* 

Quickfilver been pour'd into the inverted Syphon AG B, one of whole Legs 
A C is narrower than the other C B - 7 the Height C E, at which the Mer- 
cury ftandsin the wider LegCB, is greater than the Height CD, at which 
it ftands in the narrower Leg C A, On the contrary. Water fiands higher 
in the narrower Leg than in the wider. 




-■Experiment 4. PL 3. Fig. 23* 

■^Atmotat. A B C D reprefents a refhngular Plane of a Glaft which makes one fide 
Lea 5 L °^ a wooden Box. On the infide of this is another Glafs Plane of the fame 
fi^ e ? which, at the End A C, is prefs'd clofe to the former, and opens to a 
finall Angle at the oppofite End B D. When. Mercury is pourtl into this 
.Box to any Height as; € E, itinfinuates itfelf between the two Glafs Planes^ 
and riling to different Heights between the GlaiTes, where the opening is 
greater or lefs, it forms the common Hyperbola CG F \ one of whofe A- 
lymptoles E F is the Line on which the Surface of the Mercury in the 
Jiox, touches the inner Glafs j the other is the Line AC, in which the 
Planes are joyn'd. 

Experiment J. P£ 3 . Fig. 24* 

A B is a perpendicular SeSion thro' two glafs Planes joyn'd at A, an$ 
:0pen'd to a 'finall Angle at B \ C reprefents a pretty large Drop of Mercury, 
the larger the better, which (being made todefcend as tar as C, by holding 
the Planes in an erett Pofture, with the End A downwards) retires from the 
contaft of the Planes to D, upon inclining the Planes towards an horizon- 
tal Situation; and the Diltance CD becomes greater or lefs, as the Planes 
are more or lefs inclin'd towards the Horizon* 

200 Qo— -Jtsthe CufaMi a quarter of the increased ' Diftance~the Magneikai 
jlttraffion&z^ That excellent Philofopher Dr. Brook Taylor made fome Expe- 
riments with a touch'd Needle and a large Load-ftone that is kept in the Repo- 
fitory of the Royal Society , which, when made atfome Diftancefrom the Stone, 
agreed very well with this AfTertioii} but near the Stone, the magnetick Virtue 
did notfeem to ad according to thole Laws, which might be owing to this^ 
viz. That that Stone rather ieems to be an aggregate of Load-ftones joyn'd to- 
gether by a petreous Subftance not magnetical. For, fince that Time, by 
fome Experiments made upon it, I found that it had 15 Poles (if I may 
uie that Expreffion) or Points where the Attraffioa was ftronger than any 
Where elfe ; which Experiments, and fome: others made upon weak Load- 
Stones, made me imagine that every Load-ftone had federal Poles, or Points 
of ^Virtue on the North fide, and feveral on the South fide ; whofe Virtues 
^feeing collected by the Iron wherewith the Stone is arm'd, made an arm'd 
Load-ftone fuftain much more Iron or Steel than, the fame unarm'd. But 
% Experiments made fince, with fome good Load-ftones, efpecially, 
with a Stone of about fix Ounces, belonging to the Right Honourable the 
Lord Paizley (one of the beft in the World) I found that a good and ho- 
ifrtqgeneous Load-ftone has but two Poles/ 



A Courfe of Experimental Phihfophy. 4 r 

21. D 1.— A repellent Power in Bodies, fcc] See s'Gravefande Introduction, Annotat 
Fart I. from N°. 40 to 44. When Light is reflected from a polim'd fpe- Left I 
cular Surface of Glafs, Cryftal, or Metal ; the Particles of Light do not ftrike u^VNJ 
upon the folid Parts, and fo rebound from them ; but are repelled from the 
Surface at a finall Diftance before they touch it, by a Power extended all 
over the faid polim'd Surface. See Sir Ifaac Newton V Optics. Book II 
Part III. Prop.%. 

The Rays of Light are alfo repell'd by the Edges of Bodies as they pafs 
near them, fo as to make their Shadows, in fome Cafes, larger than they 
wou'd otherwife be. See the fame Author, Book HI. Part L where he like- 
wife proves this repulfive Force from other Phenomena. 

2 2 - D 7— ^ e f ame Part of the Tube will not fnap or give Light twice to- 
gether, in the fame Place, without a new Friclion. ] By caufing the Tube to 
fnap at the Approach of the Fingers, or any other folid Body near it the 
Eleftricity of it in that Place is alfo deftroy'd } from which we may e'afily 
iblve a Phenomenon mention'd by Dr. s'Gravefande in his Introduction. Vol. 
II. N°. 554. Thefe are his Words : 

" There is one thing remarkable and very hard to explain in this Expe- 
" riment, concerning the Direftion of Attrition^ when you rub the Tube 
« one End is held in one Hand, whilft it is rubb'dwith the other i which* 
" if it be done from the Hand that holds towards the other End' of the' 
" Tube, the Effea will not be fenfiblej but if you rub from the free End 
" of theTube towards the End held in the Hand, the contrary will hap- 
« pen. And this happens indifferently whether you hold the open or 
" ihut End of the Tube- in your Hand. 

To explain this, let us examine the Experiment by help of the roth 
Figure of Plate 2. A is the Right Hand that holds the Tube, and B the 
Left Hand that rubs the Tube, which, after moving up and down feveral 
times, makes an end of the Attrition by moving in the Direction C B A 
the Iaft Stroke : Then the Tube brought near light Bodies {Plate 2. Fig. 1 r .) 
gives Motion to them. If the laft Stroke in rubbing be made by the Moti- 
on of the Hand, from A to C, and the Hand B that went up to C quits 
the Tube in the Direction C D, without coming near it again, or letting 
the Coat-fleeve come near it, the Tube will aft upon light Bodies with the 
fame Vigour as before. But if the Left Hand, after it is come off at C, is 
brought down again carelefsly, in the Direftion C E, in a Line Parallel to 
the Tube, and pretty near it, either the Hand or the Coat-fleeve coming 
down too near, caufes the Tube to fnap (which is not heard without Atten- 
tion ) and fo deftroys the Virtue excited by Attrition, in the whole Length 
of theTube-, as the Hand A (Plate 2. Fig. 13.) does in the Place A where 
it caufes, a Snapping, which, as I faid before, will not happen twice in the 
fame Place, without a new Friction. 

23. I41.—A Glafs Globe whirVd, &c] I cannot forbear mentioning here 
a very furprizing Phenomenon in one of Mr. Hauksfois Experiments. He 



42 A Couffe of Experimental Phibfophy* 

Annotat coated with Sealing-wax the Infide of one Hemifphere of one of his Glafs 
Left. I. Globes to fuch a Thicknels, as to render it perfe&ly opaque : Yet when this 
i*/~*V~\J Glafs was exhaufted of its Air 3 and whirPd round s where the Hand was ap- 
ply'don the Outfide to give an Attrition to the Globe, the Wax became 
as tranfparent as the Glafs it felf, the reft of the Globe that had Wax re- 
maining opaque, where it did not touch the Hand, though the Moment 
before it had been tranfparent as it pafs'd under the Hand. 

A View of the 25th Fig, of PL 3. will reprefent the Thing fully. 
The Hemifphere ACB of the Glafs Globe GACB is made opaque, by 
being lin'd with Wax on the Infide, whilft AGB is clear Glafs. The Glafs 
is exhaufted of its Air by means of the Cock D \ then being fet between 
the Pillars EF, it is whirfd fwiftly round by means of the Wheel K, whole 
String goes round a Pulley P fix'd to the Brafs Socket, whole Shank is the 
Axis of the Globe, jfhe Screw H draws forward the other Pulley I, to keep 
the Wheel-firing always tights 

When the Hand is apply'd at C, its Infide becomes vifible, through the 
Wax on the concave Side of the lin'd Globe, the reft of the Wax remain- 
ing opaque 3 lb that the Hand cannot be leen by an Eye at Q^, but by an 
Eye at O looking at it through the unlin'd Part of the Glafs at G. 

■24. — • though the Caufes of thefe Caufes are not known, &c. ] When 
Genealogifts, in fearching into the Original of Families, are got as far as 
they can, and have found the firft of the Family, fo calPd, becaufe they can- 
not difcover who were his Parents: It wou'd be very abfurd to fay, that 
becaufe the Father of this Firft ( which for Example we will call John) 
is not known, therefore John is not the Father of Peter , the Grand-father 

of William, and Great Grand-father of Nicholas, &c.« Which was provU 

before, by fuch Evidence as is proper in that Cafe. So when it appears by 
Obfervation that Gravity is the Caufe of the Fall of heavy Bodies, which 
obferve certain Laws in their Motion < — -That a heavy Body by its De- 
scent moves the Axis a of Wheel, that carries round another by its Teeth,, 
which by the Intermediation of other Wheels and Pinions, carries round 
a Hand upon a Dial- Plate to meafure Time, or for other U'icsj it wou'd 
be very unphilofophical to fay- — -That our Reafoning about the Caufe of 
the Motion of the Hand is falfe, as being founded upon occult Qualities % 
becaufe we can go no higher than Gravity^ whole Caufe we don't pretend 
to know. 



t v r 5, 

JLj JuU \jr 



LECTURE II. 



j s f ,L, 1 1 HE Momentum ox Quantity of Motion in Bodies (fome-Le£h 
I times called (imply Motion) is that Force with which Bo- 
dies change their Place. 
I don't mean the Stroke^ Preffure, Tra£Uon, or any other Ac- 
tion which caufes this Change of Place in a Body ; but the Force 
which it has all the while it is-moving from one Place to another* 

2. Thi s moving Force may always be known by the Eflfed which 
it is able to produce ; that is, by the Stroke which the moving Bo- 
dy can give, or by the Refiftance or Gbftacle which it is able to 6'- 
vercome. 

3. This Quantity of Motion r which is the Meafure of the Force, 
is made up of the Quantity of Matter and the Velocity taken toge« 
ther. That is, when we compare the Momenta,, moving Forces, 
or Quantities of Motion in Bodies, we multiply the Mafs or Quan- 
tity of Matter in each Body by its Velocity *. *-Annot. 

4. Velocity or Celerity , is the Swiftnefs with which a moving 
Body changes its Place ; and may always be known by thVSpace 
that the Body goes through in a given Time. 

5. The Quantity of Motion may be encreas'd ; either by encreaf- 
ing the Quantity of Matter, which is mov'd with a determinate 
Velocity ; or keeping the fame Quantity of Matter, and encreafing 
the Velocity ; or by encreafing both. — And in the three Cafes it 
is done by applying more Force; for here * Force zn&Motion mean* Annot. 
the fame Thing. 

6. The Motion of any Whole, is the Sum of the Motion of all 
the Parts ; and therefore (as we faid before) it becomes doubled in 
a double Body mov'd with equal Velocity, and quadrupled in a 
double Body mov'd with a double Velocity. 

7. If a Man with a determinate Force throws from him a Weight 
of 50 Pounds to the Diftance of ten Feet j lie muft apply twice the 

G % Force 



Fig. i. 



44 A Courfe of Experimental Philofophy 

Leer. II. Force to throw a Weight of 100 Pounds to the fame Diftance, or 
^"V^ to throw the 50 Pound Weight twice as far ; but if he ufes no more 
Force than he did before, he will throw the 100 Pound Weight 
only to the Diftance of 5 Feet, and then the two Bodies will have 
the fame Quantity of Motion; becaufe 50 multiplied by 10, or 
100 multiplied by 5, give the fame ProduS, viz. 500. 

Experiment I. Tl. 4. Fig. 1. 

8. ABCDE is an Inftrument contriv'd for ill uft rating what has 
been faid, and diftinguiftiing Motion and Velocity, which fome 
Authors have confounded. The rabbeted Cheeks BD, CE, ai e fo 
contrived that the fmooth cylindrick Weight K or L (the one of 8, 
the other of 4 Ounces) may move between them with very little 
Friction. Let the Spring AB be bent to a certain Degree, by flip- 
ping the Knot G of the String faften'd to B upon the Catch of the 
Iron F ; then lay on the Weight L at B, which upon letting go the 
Spring, by lifting up the Knot, will be fhot from B to the Point I, 
which is 24 Inches from B. If the Cylinder K be fhot in the fame 
Manner, it will go but to H 12 Inches from B. 

\ That the Quantity of Motion is the fame in both Bodies, is e- 
vident, becaufe the Spring is equally bent in both Cafes; and that 
thofe Quantities of Motion are made up of the MaiTes mutiplied 
into the Velocities is alfo evident, becaufe L= 4 Ounces X by BI 
(24) its Velocity gives 96, equal to K (8 Ounces) X BH (12) its 
Velocity. 

But if you would have K driven as far as the Point I, to which 
L was driven ; the Spring muft be bent with a double Force, and 
then K will have double the Motion that it had. N. B. This Ex- 
periment is made ufe of rather to illujirate this Matter than to 
prove it. ' 

^ 9. Hence it follows, that any little Body may have as much Mo- 
tion as a great one, be their Difproportion what it will ; provided 
that the Velocities that are given them be reciprocally proportio- 
nable to their MaiTes ; that is, if the little Body has as much more 
Velocity than the great one as it has lefs Matter. 

This is the Reafon why, fince the Invention of Gun-Powder, 
battering Rams have been difus'd in War ; for thofe and other hea- 
vy Machines managed by a great many Hands, and mov'd againft 
a Wall with little Velocity, did no more than now is perform'd by 

a fmall 



A Comfexf Experimental Phihfophy. 45 

a fmall Cannon-Ball, three or four Men only being employed to Left. TL 
manage the Cannon* If the Ball weighing 56 Pounds be flbot ^VV 
out of the Cannon C, againft the Wall AHGE fo as to ftrike it atl. pi# 4 * 
L, it will produce the fame Effe£fc as the battering Ram R, which * S " 
weighs 41 112 Pounds i provided that the Cannon-Bali moves as 
many times fwifter, as it has lefs Matter than the Ram. See the 
Calculation of it in the Notes \. I A nn , ?e 

If a fmall Piftol Bullet fhou'd move with the fame Velocity as 
Light, it would ftrike as ftrongly againft an immoveable Obftacle 
as a Cannon-Bail 700000 times as big ; becaufe Light moves 700000 
times fafter than a Cannon-BalL Light is about 8 Minutes coming 
from the Sun, and a Cannon Ball wouM ipend ten Years in going, 
thro 7 the fame Space. 

10. As the Quantity of Matter in a moving Body, multiplied by 
its Velocity, v gives us the Quantity of Motion : So the Quantity 
of Motion divided by the Velocity, will give us the Quantity of 
Matter ; but if it be divided by the Quantity of Matter, it will give 
us the Velocity. If feveral Bodies of different Weights move with 
equal Velocity, their Motions will be to one another as their Quan- 
tity of Matter. 

1 1. Hen ce may be deduced an unanfwerable Argument for a Va- 
cuum. For if all Bodies, abftrafting from the Refiftance of the 
Air, move downwards with the fame Velocity, as has been prov- 
ed*, their Motions comparM will be refpe&ively as their Quantir * L. 1. 
ties of Matter; but the Motion downwards, or Force which drives Na *> 9 " 
them to the Earth, is their Gravity; therefore we find the Quanti- 
ty of Matter in any Body by its Gravity, which muft always be 
proportionable to it* Now if two Bodies of equal Bulk weigh dif- 
ferently, as we find by Experience they do, there muft be Vacuities 
interfpeiVd in the lighter: As for Example, if there be two Inch 
Cubes A and Bf, and the Cube A be of Silver, whilft the Cubef pi ate ^ 
B is of Cork ; it will be found that A weighs 40 times more than Fig. 7. 
B, therefore B has 40 times lefs Matter and ought to be 40 times 

lets in Bulk, if it had no Vacuities; for if it be anfwer'd that the Voids 

or Pores of the Cork are filled with Air and fubtile Matter ; that 

Air and fubtile Matter* together with the Cork ought to weigh* Ann. 44 

as muclxas the Silver; or elfe the two Cubes cannot be equally 

full* 




Left, II- it. The whole EfFed of mechanical Engines (whereby Moti- 
^OTV/on is given or ftopp'd, or a Refiftance is overcome) depends up- 
on what we faid above, N. 9. 

If a- great Weight is to 
trive to give the little one fo much more Velocity than the great 
one as it has lefs Matter, and then its Force being equal to that 
of the great one, it will fuftain it, if they move in contrary Di- 
rections ; becaufe then equal Forces will deftroy each other. This 
is done by the Contrivance of the Engines, and Manner of apply- 
ing them. ^ For if the Velocity of the great Weight be determin'd 
as well as its Quantity of Matter, and the Quantity of Matter ia 
the little one; then the Velocity of the little one (which in this 
Cafe is called the Power) mult be encreafed in the Proportion 
above-mention'd. But if the Velocity of the Power be determine 
then that of the Weight muft be diminifhM in the faid Proportion : 
The Engines for thofe Purpofes being always fo contrivM, that the 
Weight or Power may he applied in fuch manner as to render their 
Velocities reciprocally proportionable to their MalTes. 

Experiment II. Tlate 4. Fig. g, 

Plate 4a ig. Let AB be a Leaver or Balance divided into 20 equal Parts 5 
Fig. 3° whofe Center of Motion is at C; if the Weight W of 200 
Pounds hangs by an immoveable Hook at A, and we would fuf- 
tain or keep it in Mquilihrio by means of the Power or fmall 
Weight P of 50 Founds ; it is plain that it has not Force enough 
at E to fuftain the Weight W, becaufe in the Motion of the Leaver 
the Point E and A will defcribe not only fimilar but equal Arcs 
E e and ka\ fo that when W moves 1 Inch, P will only move r 
Inch j and fince the Velocities being equal, the Quantities of Mo- 
■*No. 10. tion or Forces are as the MafTes *, the Weight W will always 
overpower, as having 4 times the Mafs of P. But if P be re- 
mo vM to B, then it will defcribe an Arc fimilar to, but 4 times 
greater than that which W defcribes ; that is, it will defcend 4 
times fafter than W rifes : If then its Velocity be 4, and that of W 
only 1, f or 50 multiplied by its Velocity 4 will give 200 ; which 
is equal to the Product of W, or 200 multiplied by its Velocity 1. 

14. But if the Power P had been immoveable at E, and the 
Weight W moveable; an MquUthrium would have been had by 
diminifihing the Velocity of the Weight in bringing it forward to 

■D, 




A CourJe of Experimental Philofophy. 

D, where being 4 times nearer to the Center than P, it would have Led. II. 
had 4 times lefs Velocity. L/"V~nj 

t 5. If both the Weights had been moveable, and P had been but 
12 Pounds and an half, then the Velocity of P muft have encreas'd 
by removing it to B the 16th Divifion, at the fame time as that of 
W was diminifh'd by bringing it to D the firft Divifion on the o- 
ther Side of the Center; for then W (200) multiplied into DC 
(1) which is proportionable to its Velocity, wou'd have given 
200, which is equal to the Produft of / (121) multiplied into BC 
(16) its Diftance from the Center, which exprelTes its Velocity. 
If therefore the Power has a little more Velocity given it, than in 
a reciprocal Proportion of the Mall'es, it will have more Force 
than the Weight, antTcbn,fequently raife it, whereas it only fuf- 
tain'd it before. 

16. Thus by means of a Leaver, a Man, whofe natural Strength' 
does not exceed 200 Pounds, fhall acquire fo much relative Force 
as to raife a Stone of 2000 Pounds by applying bis Leaver fo as to 
render the Velocity of the Stone ten times lefs than that of his 
Body at the oppofite End of the Leaver, which in that Cafe will 
be ten times farther from the Fulcrum or propping Point, than the 
Place where the Stone is applied. For if a Man by his natural 
Strength can raife 200 Pounds with a determinate Velocity, there 
is no Engine in the World that fhall enable him to raife a 000 
Pounds with the fame Velocity; but he muft do it with the 10th 
Part of that Velocity. If he muft employ 10 Seconds of Time to, 
raife 2 00 Pound io Foot ; and wou'd raife a Stone of 2000 Pound 
Weight by a Leaver whofe Brachia (or Lengths on each fide the 
Center of Motion ) are as 10 and 1 ; he muft move 10 Foot at the 
End of the long Brachium of the Leaver whilft the Stone moves 
1 Foot, which comes to the fame as if the Stone being cut into 10 
Pieces, each of them was fucceffively lifted up one Foot by the 
fame Man, who wou'd do it )uft with the fame Labour as when 

he rais'd it all at once with the Leaver * * knxi. n 

We cannot alter Nature ; where we wou'd gain Strength we 
muft lofe Time > and where we wou'd gain Time we muft employ 
more Strength f. t Ann ^ 

17. If the Velocity of the Weight, as well as its Quantity of 
Matter, be. determin'd ? and lilsewife the Verity of the Power 



48 A Courfe of Experimental PhUofiphy^ 



Le£t. II. then if the Power is notfufficient to raife the Weight, there muft be 
more Matter added to it, till the Produtt of its whole Mafs mul- 
tiplied into its Velocity be equal to the Produ£t of the Mafs of the 

* PL 4. Weight into its Velocity. If, for example, the Weight * W ftill 
Fl &- fuppofed equal to 200 Pounds be fixed at A, and the Power/ equal 

only to 1 2i Pounds be fix'd at B; it will not be poftible for the faid 
Power to fuftain the Weight, till its Quantity of Matter be qua- 
drupled to make it 50 Pounds, and then 50 X 16 will be equal 
to 200 X 4 ; becaufe here the Diftances are as the Velocities, 

Sometimes it is required to give a heavy Body or Weight a 
confiderable Degree of Velocity, as when the Ancients ufed to throw 
great Stones with thofe kind of Baliftte which they calPd Scorpi- 
*Ann. 7. ons ; and then the Power muft be coafiderably greater than the 
Weight ; for as it is applied nearer the Center of Motion than the 
Weight to be thrown, it muft be heavier in a reciprocal Proporti- 
on of thofe Diftances when the Weight is only fuftain'd, arid-much 

# Ann. ibid, heavier to give the ProjeQile Body a fufficient Velocity * But 

thefe Things will be better underftood as w T e come to confider the 
mechanical Towers and the Uiesot firnple and compound HngL es ; 
in order to which we muft explain fome Terms, and take notice of 
Tome Truths neceffary to be known by every Engineer, 

Definitions. 

18. A Weight is any Body to be fuftain'd, raifed or deprefs'd, 
pufh'd or drawn, or mov'd in any manner ; fo that the Expreffion 
to raife a Weight is very extenfive in the mechanical Senfe ; as 
fometimes it is applied to the driving a Pile into the Ground ; fome- 
times to the flopping of a Body in Motion, as the running of 
Water, &c. 

19. A Power is whatever is made ufe of to raife a Weight in the 
Senfe above-mention 7 d, whether the Power it felf be a heavy Body, 
a Spring, the Motion of Water, Air, Smoke, Flame, or Preffure 
of Steam excited by Fire from Liquids ; or the Force of any A- 
nimal, a£ting by its Strength or Weight, or both. 

20* The Intensity of a Tower is its abfolute Force, that is, its 
Force, fuppofing its Velocity equal to that of the Weight ; for its 
Moving or ABing Force may be greater or lefs, according as its 
Velocity is encreasM or diminiftfd, in refpedt of that of the Weight- 
As for Example, If 



A Cmrfe of ExperimmalPH 4p 

If a Mm be the Power, and can raife from the Ground a cer- Left. -II. 
tain Weight, that Weight will exprefs or be equal to the Inten- 
fity of * the Power ; for in this Cafe, whatever Engine be made 
life of, that Part of the Engine, where the Weight is duly applied, 
will move juft as faft as that which a Man a&s upon with his 
whole Force. So if a Man can prefs upon the Point E, at the 
4th Divifion of the Balance AB * with the Force of 200 Pounds, * PUFi 
he will juft fuftain the Weight W, or 200 Pounds, hanging pre- 
cifely as far on the Other Side of the Center or Motion* 

21. The Line of T>irettion\s that Line in which a Weight or 
Power a£ts, or endeavours to a£l *v *Ann.8, 

22. A Power may a£t in any Dire£Hon whatever ; but a Weight 
has but one Dire£Hon, which is towards the Center of the Earth, 
in which Dire&ion all heavy Bodies endeavour to defcend, and 
a£hially do, when no Obftacle hinders: So that the Line of 
IDireffiion of a Weight is a Line drawn from its Center of Gravity 
to the Center of the Earth. 

23. The Center of Motion is that Point round which a Body or 
a Machine moves, or endeavours to move when it cannot or does 
not turn quite round ; and in that Cafe, all the Points of the 
Body defcribe Circles, or Arcs of Circles, about the Center of 
Motion. This Center may be taken any where according to the 
Make of the Engine. 

24. The Center of Gravity is a Point about which all the 
Parts of a Body are in Mquilibrio. It is confider'd as the Middle 
of the Weight of the Body, though often it is not the Middle of 
the Body it felf ; and if the Body be fufpended by that Point, it 
will hang in any Pofition ; otherwife the Center of Gravity will 
defcend as low as it can. 

Ex PE RIM ENT III. ■ jP/. 4. Fig. 4. 

25. BQ/is a round Board fufpended by its Center C on the 
Points of the fpringing Calibers A. In turning the Board round, 
the two Marks made upon it K and Q, defcribe the Circles Kk 9 
and round the Center of Motion C, which is here the Cen- 
ter of Magnitude : If the Center of Motion was taken in any 

H Point 



0 ji Cmrfi of Mxptriweitfd 

Le£t. II. Point which is not the Center of Magnitude, as at c ftill K and 
^TV^V CL would defcribe Circles about the Center of Motion* though 
FiJ"? 4 ' t he Center of Magnitude wpuM not then be their common Cen- 
5 * ter, but itfelf would defcribe a Circle as C d about c 3 the Center 
of Motion. If the Body fufpended does not go quite round, as 
here the Side R flops againft the Top of the Calibers at q \ inftead 
of Circles, the Points K and Q defcribe only Arcs of the 
Circles K^, Qd* 

* Plate 4. 26. If C * be the Center of Gravity of the Body, and the 
Fl S-> Ppdy be fufpended by it, and made to turn round that Point, it 

may be ftoppM in any Pofition of the Points K and and it will 

* Plate 4. then remain at reft ; but if the Body be fufpended by c, * which is 
F! g- 5» not the Center qf Gravity, then the Center of Gravity C will 

defceijd as low as it can to C. 

* Plate 4. But if c * b? the Center of Gravity* and placed direffily over 
Fig, 6. the Center of Motion YLj the Bad} wk * remain in that Tpfitionj 

beqaufe as the Center of Gravity endeavours to defeend in the 
Line e K, which is the Line of Direction of the Body (in which 
Line the Point K is fupported) it prelfes direftly upon the Point K, 
which \s fu ftainM by the CaUbers ; but if the Body ke mowed ever 
Ja /gttej fo as to bring the Center of Gravity f towards d or e f 
the B#d$ will, turn and not reft till the Qenter of Gratuity wwe$ to 
%/L dire fitly nnder the Center of MQtim y the Body fyjijig latp the 
Eitipa i " ~ 




Experiment. IV. Tl. 4. Fig. 8V, 

27?. HSekce n\ay fee ckdgcM % Mefehod far finding tli£ Center 
* .j$m. 9. of Gravity pf any Body ^e<?h$nica$y *, Let AR be a Body 
f ; Hate 4. vvfhofb Cei^ei; of Qravity is to bg foind- If it be fufpended bf 
& any Part as A, fo as to mov§ hsoly upp%ths Pin at A, and a Plunifr 
Line A P hangs from the fame Pin, its Center of Gravity C mui 
be under, or rather behind that Line ; becaufe it will fall below the 
Center of Motion A ; Let that Linf AB be marked upon the Body^ 
as m Fig. 9, and then fufpend the Body by any other Part, as F ; 
pravicj^d th^the Center of option, be not in the alcove- mentioned 
Ling Hang on the Plummet at F, and the Line. ED ; under the 
Plumb-Line FP ^ilkut the Lme : A3, and fliew the Center of Gra- 
vity to, be at C ; for fince it mu| be both in the Line AB and in 
the Line FDi it can, only be in the Point C where they interfe£L 



A Cm ft of Experimental Philq/bphy. $ t 

H. B. W ? have not here confider r d the Thicknifs of the Body $ Le£r. it 
but if we fnppofe it a 'Piece of Board as the Figure reprefents ; K *ry~>J 
then we nmfi only make the fame Experiment on the' other Side, 
and we f hail find another 'Point C juft off ope to the fiffiToin*t 
C. The Line which joins thefe two Toints will be the Axis of 
Gravity, and the middle of that Line the Center of Gravity. 

28. Hence alfo follows, That let the Figure of a Body be 
what it will, the Body can't fall when its Center of Gravity h 
fuftain'd; and when any Body is in JEquUibrio, its Center of 
Gravity muft be in a Line which goes thro' the Center of Mo- 
tion and the Center of the Earth ,• which is the Line of Diredion of 
heavy Bodies mentioned before * Thus in Fig. 7. f where the* 21 . 
Tobacco-pipe is fuftained in Mquilibrio upon one's Finger, thet P1 -*- 
Point C juft over the Finger is the Center of Gravity. 

E x P E R I'M E N T V. SP/. 4. 

In Bodies that are both regular and homogeneous, the 
Center of Gravity is juft in the middle of the Body ; that is, in 
its Center of Magnitude; as appears in the Body AB *, which* Plate 4. 
being fufpended by its Center of Magnitude C, then turn'd Fi 8- 4- 
round, will remain in any Pofition in which it is ftopp'd ; but in 

5- * where the fame Body is fufpended by another Point c. it* Plate 4 
will not reft but when the Point C is come down below r, or is 
dire&ly above it, as we faid before. But if the fame Body, which 
was fuppos'd a circular Piece of Wood (as for example of Oak} 
be denfec in one Part than another, or be made fo by letting a 
Piece ef Lead into the Wood as at M (Fig. 6. *) then the Cen- * Plate 4, 
ter of Gravity will no longer be at C, but at K ; about which 
Point of Sufpenfion only, the Body will remain in any given Pofiti- 
on. If the Body was fufpended by the Point C, it wou'd be at reft 
only in two Pofitions; viz. when the Lead being carried up to I 
the Center of Gravity is at or when the Lead is at M, and* 14 
the Center of Gravity atK*. If the Body was homogeneous * 4'. 
but not regular, the Center of Gravity wou'd alfo then be diffe- 
rent from the Center of Magnitude. As for example, If you take 
the Pipe of Fig. 7.* and break it at C its Center of Gravity,* Plate 4. 
you will find by weighing the two Pieces fueceffively, that there 
is more Matter in the half CB, than in the other half or 
Shank AG. 

H 2 go. As 



5 2 A Courfe of Experimental Thifofiphy. 

Left. XL go.- .As- any Body that we confider in Mechanics, is only an 
VVNJ Aggregate of feveral other Bodies or Parts: So the Center of 
Gravity of a Body is only the common Center of Gravity of all 
its Parts ; and confequently if feveral Bodies are united in any 
Machine; or if there be any Combination of Bodies to be fuftain- 
ed, regard is no longer had to the particular Centers of Gravity 
of the feveral Bodies which make up the Compound, but only to 
the common Center of Gravity of the Who e. Thus a Wind- 
mill muft be fupported under the common Center of Gravity of 
all its Parts, and its Line of Dirc£tion muft fall along the Axis 
of the Poft round which it moves: And a Crane upon a Wharf 
or a Dock (where the whole Machine turns round) muft have 
the Line of Dire&ion in its Axis *. 



^9 



* ; Ann, i t. 



'Of 



Experiment VL TL 4. Fig. io*. 

31. Let the Line AB reprefent an even Rod or Wire divided 
into two equal Parts at the Point C; its Center of Gravity wilt 
be at C And if two equal Bodies equally heavy We thruftion 
upon its Ends, fo as to have their Centers ot Gravity at the fame 
Diftance from C, they will be in Mquilibrio about the laid Point 
which will then become their common Center of Gravity^ and 
continue lb whether the Bodies approach nearer to, or recede 
farther from it in Proportion to their Mafles. The fame will 
happen if the Bodies are unequal as A and B r whofe Mafles are 
to each other as.'Two and One,, provided that the greater Body be 
at A twice nearer to the common Center of Gravity c than the 
lefler Body B: And c will ftill be the Center of Gravity of thole 
Bodies, tho r they fhou'd move to immenfe Diftances from each 
©ther, provided their Diftances from the faid Point are recipn> 
cally as their Mafles,, as., we laid, before^ 

32. So that when two Bodies approach towards or recede from 
each other, with Velocities reciprocally proportionable to theiu 
Mafles, their Center of Gravity will remain at teft. And if the 
Bodies being made faft upon the Wire, the Center of Gravity be 
fuftain r d by a Pivot or pointed Broach,Jiow fwift Ibever the Bodies 
be made to turn round the Center of Gravity and each other, the 
Center of Gravity will remain at reft *, and the Bodies will de- 
fcribe fimilar Circles about it and about each other, the one 
inever oTCr-gowering the other *. If they be carried forward in 

any 



A Courfe of Experiment d TUlofophy. g * 

any manner by any external Force afting upon them in propor- Left. IL 
tion to their ^Mafles, their Center of Gravity will go forward uni-\/Y"W, 
for ml y in a right Line, and move juft as if the two Bodies were li- 
nked into one at the faid Center : And if they be projected, their 
Center of Gravity will move in the fame Curve as all Projectiles 
do, whether in their Motion they turn round each other or not, 
This is evident in the Motion of an Arrow, of Chain-fhot, or 
Bar-fliot, and of a Stick thrown from the Hand, the Center of 
Gravity of any of thefe Bodies moving in the fame Manner as a 
fingle Ball wou'd do. So the Moon and Earth, in their Motion 
round the Sun, do neither of them defcribe the Magnus Or bis - r 
but their common Center of Gravity defcribes it, in the fame man- 
ner that they wou'd do if they were both united in that Point, or 
in the fame Manner that the Earth alone is fuppos'd to do it, when 
thefe Inequalities of Motion are overlooked, and provided that 
their Diftances from their common Center of Gravity be reciprocal- 
ly proportionable to their Mafles; their Diftances from each other 
may be greater or lefs in any Proportion : If there were no o- 
ther Bodies in our Syftem but the Earth and Moon turning round 
each other, their Center of Gravity wou'd always remain at reft. 

Experiment VII. PL 4. Fig. 11. 

33. If to the two Bodies A and B there be added a third at D*jPi. 4* 
equal to one of the other, let A and B be reduced to their commons's- 
Center of Gravity, and be conftdered as a Body equal to both placed 

at C; then the common Center of Gravity of C and D will be found 
at K*, as much nearer to C as the Mafs of the Body or Bodies at* 3-xs 
C exceeds that of the Body at D. If the new Body weighed but half 
as much as the others, it muft be removed to d, fo as to have the 
Diftance Kd, quadruple the Diftance KC. Now if CD be a 
Wire, and it be fupported under K, the three Bodies, whether D 
or d be made ufe of, will be fuftained by that means; only in ta~ 
king the Center of Gravity exactly at K, we muft not confider the: 
Weight of the Wire, whofe Thicknefs we are tofuppofe diminifh- 
ed in infinitum, as to look upon the Wire only as a Mathemaci*- 
eal Line without Subftance or Weight.. 

Experim ent VIII. PI. 4* Fig.. 1?.. 

34. If upon this Center of Gravity of the three Bodies, be pla<~ 
ced a. flat triangular Body abc with its Center of Gravity juft. 



|4 Gmjk of M^p^mMal Phihfiphy, 

.Left, XLfover K, then a fipare om m £efg> then a circular one as ■&■//, 
^VV jail in the fame manner ftrlt the whole will be fuftaiaM by fupport- 
ing the Point K. Wh# nee; it appears, that if the whole Weight of 
a Body he red-weed into its Center of Gravity, it will (a<a as a heavy 
Body,; that v£)grm)kate juft in the lame manner as it wou'd before 

35- I F thele three Bodies, united to or acting upon one another 
in any manner proportionable to their Mafles, be carried round their 
common Center of Gra vity ; that Point will be at reft, for the lame 
Reafon as it will happen in refpeft of two Bodies becaufe any 
Number of Bodies may in this refpe£fc be reduced to two. Thus 
in our Syftem, where the Sun and all the Planets move round their 
common Center of Gravity, that Center is at reft in the middle of 
the Syftem> Tho 1 we commonly confider the Sun as immovable in 
the middle of the Syftem; becaufe as it has vaftly more Matter 
than all the Planets together, that Center will always be very near 
*he §un ? s Center 

It o&m happens that the Center of Gravity of a B©dy, or 
of a %ft$m of Bodies* is not withimthe Body itlelfy or any one of 
the combined Bodies ; yet we are to have the fame Regard to its 
Support, Defeont,, or Motion, in any Bireftion, as if it was. As 
Z? L>4 : for example, let us fuppofe the Bodies A and £ * tobeatthe Di- 
Ip * ftance A A from each other, and that aB is, no longer a Wire but 
A b is a Line reprefenting their Pittance ; we ffiall find their Cen- 
ter of Gravity to be at c without the Bodies . And if inftead of th€ 
■* Pi. 4- Wire CD , we fuppofe the Body D * joined to the two Bodies A 
Fig, m. and B by the Wires AD and BD, the Center of Gravity at K will 
foe neither in the Bodies nor Wire ; fb that if we wo.u'd (iiftain the 
laid Bodies we muft fupport {bme one of them, or fome Part of the 
Wire as G, which being madb the Center of Motion, the Center 
of Gravity K will (if the Bodies hang freely) come juft under it ; 
or if we fupport the Point H, the Bodies will be at reft by reafon 
of the Center of Gravity being juft over H the Center of Motion. 
** 'Pi. -4* In the Ring ABH * the Center of Gravity is in no Part of it, but 
Fi S- ^ it may be fupported by any other Point as O or E, &c. Upon this 
Account the Ring of Saturn has its Center of Gravity in the Bo- 
dy of Saturn. And tho' the common Center of Gravity of the 
Sun, Moon, and Earth is within the Sun's Body, yet the common 
Center of Gravity of the Moon and Earth is in neither of the 
Bodies, hut between them. 

35« Since 



3 5« Since OE is the Line of Dire&ion, it is evident that in a-Le£t. it 
■ny Pofition of a Body or of a Combination of Bodies, If the Tdini 

o'f Sufpenfion or Center of Motion be in any Tart of the Line m 
'Direction, the Body or Bodies will remain in that Tofitiou ; others 
wife the Center of Gravity will de fiend as low as it can y and fry hi- 
Motion alter the Tofition of the Body. 

Experiments IX and%, 

36. Several odd Thmomena depend upon this Principle | as for 
example, the double Cone or Spindle ACBD* being laid on at E* Pi. 4 
upon the lower Part of the Rulers EF will of itfelf move towards Fig." 14,, 
FF, tho' thofe Ends are raifed up to the Heights FG by the two 
Screws FG ; and by that means will feem to move upwards : And 

the Cy linder M *, whofe Center of Gravity is in the Mid- way be- * Pi. 44. 
tween K and O, will a&ualiy roll up the inclin'd Plane AC, pro- Fig. 15. 
vided it be hinder'd from Aiding by the Rope Rn How high FG* * F, 14. 
may be in proportion to the Bignefs of the Spindle ABCD ; or; 
EC* in proportion to the Cylinder M,,is demonftrated in the* F; 15* 
Notes . * Ann. i2« 

37. But- before we mention any more of xM^eTJMnomena^ it 
will not be amifs to fhew how the common Center of Gravity of* 
two or more Bodies may be found 

In two Bodies it is in a Line which joins their particular Ceti«~ 
ters of Gravity, and this Analogy gives it. 

jts the Mafs of (or Quantity of Matter inj the two Bodies 

Is' to the Maff of one of the Bodies;: 
So is the Uiftance •of the ' Centers of Gravity of the Bodies: 

Th the "Defiance of the common Center of Gravity from the Cem- 
ter of Gravity of the otket Body. 

For example, if we foppofe.the Bodies A and B* to weigh * pi; 4.,;. 
2 Pounds each, and to have their refpe&ive Centers - of GravitjfTig.'i.o^ 
4 Foot difent from each other ; then, 

4 the Mafs of the two Bodies : • 
Is to 2 the Mafs of the Body B:: 

So is AB, or 4, the Dijtance of their two Center s of Gravity %i 
To AC, the Difiance of the common Center of Gravity from^i 
the Center of Gravity of A, which if 2 Foot, 



$6 A Cowfe of Experimental Philofophy, 



Led:. II. Or to exprefs it fhort by Algebraical Notations AH~B : B ;: AB; 

W^V~W AC ; but if we take A of 2 Pounds and b of 1 Pound, and A& 9 
equal to 9 Feet, the common Center of Gravity will be at c with- 
in 1 Foot of A, or twice nearer its Center than the Center of h ; 
becaufe A-f-£ (9): £(1) A£ (5): Ar(i).Thus is thecommon Cen- 
ter of Gravity of the Moon and Earth found, when once we know 
their Mafles and Diftances. The Earth weighs about 40 times 
more than the Moon, and the Center of the Moon is about 61 
Semi-diameters of the Earth diftant from the Earth's Center ; there- 
fore the common Center of Gravity of both is diftant from the 
Center of the Earth almoft one Semidiameter arid a half, or near 
2000 Miles above the Surface of the Earth ; for as the Mafs of the 
Earth and Moon (41) : to the Mafs of the Moon (1) :: ib is their 
Diftance (61): to the Diftance of the common Center of Gra vity 
of both from the Center of Gravity of the Earth, that is, iff- Se« 
midiameter of the Earth. 

38. If there be more Bodies than two, as for example, the three 
y; g< zu Bodies A, B, and D* ; firft find the common Center of Gravity of 

two of them by the foregoing Rule, and it will be at C ; then fay, 

As the Mafs of the two Bodies confdered as united at Cj toge* 

ther with the Body D : 
Is to the Body D :: 

So is CD the diftance of the common Center of Gravity of A andB 

from the Center of Gravity of C : 
To CK, the'Dijiance of the common Center of Gravity of the three 
Bodies from the common Center of Gravity of the two firft. 

Or in fhort A+B+-D : D:: CD: CK. And if there be a 
Combination or Syftem of any Number of Bodies ; their common 
Center of Gravity may be found, Step by Step, in the fame 
* Ann. 13. Manner *. 

39. Hence follows, that one may alter the Place of the Center 
of Gravity of a Syftem of Bodies, by adding one or more Bodies 
to it, or by taking one or more of the Bodies away. And the 
Center of Gravity of a fingle Body may be removed at plea- 
lure, by adding to or taking from its Mafs. And this is of 
lingular Ufe in Machinery or that Part of Mechanics that relates 
chiefly to Engines, bccaufe of the fc veral Powers that are combined 

in 



A Courfe of Experimental Pbilqfophy. 5 7 

In a Machine, and the feveral Pofitions that they mull have in re- Led. II 
fpect to each other in their Motions, vyv 

Experiment XI. Tlate 5. Fig. 1. 

40. AB* is a rolling Lamp that has within it the two moveable * Pi. 5. 
Circles DE and EG, whole common Center of Motion is at K, Fi &- 
where their Axes of Motion crofs one another, in which Point 
alfo is their common Center of Gravity. If to the inward Circle 
you join withinfide the Lamp KCmade pretty heavy and movea- 
ble about its Axis HI, and whofe Center of Gravity is at C, the 
common Center of Gravity of the whole Machine will fall between 
Kand C, and by reafon of the Pivots A, B, D, E, H, I, will 
be al ways at Liberty to defcend ; and therefore let the whole Lamp 
be roll'd along the Ground or movM in any manner, the Flame 
will always be uppermoft, and the Oil cannot fpill. Thus is the 
Compafs hung at Sea ; and thus fhou'd all the Moon-Lanterns be 
made that are carried upon a Pole before Coaches or Carriages that 
go in the Night. 



Experiment XII. TV. 5 . Fig. 1. 

41. When inclin'd Bodies, fuch as the oblique Cylinders ABED*,!* PL 5. 
ah ed, are fet upon an horizontal Plane; they will faU the Wayps- 2 - 
that they incline, if in their Motion that Way, their Center off 
Gravity can defcend without firft riling *. Thus c, which is the * a*. 
Center of Gravity of the Body abe d, will defcend in the Arc^, ! 
whofe Center is the Point which is the Center of Motion of the 
Body when it falls. But C the Center of Gravity of the Body 
ABED moving round the Center of Motion E in the Arc CK, 
cannot come down to K without firft riling up to F which is a- 
bove C ; therefore the Body can't fall by its own Gravity, becaufe 

the Center of Gravity will not rile of itfelf*. * a4? a 

42. Here it is obfervable that co the Line of Direction * of the * *o. 
Body abedhWs without its Bafe : And CO the Line of Direction 

of ABED falls within its Bafe ; whence it follows, thaffinclin'd 
Bodies fet upon an horizontal Plane will fall, when their Line of 
Dire&ion does not go thro' their Bafe 5 but they will ftand when 
the Line of Direction falls within their Bafe *. 




ji QwJe of Experiment d 

Le£t. II. This is the Reafon why an inclin'd Tower, fuch as that of Tifa 
&SV*s} or Bologna, does not fall, tho' its Top hangs fo far over the Bafe 
* Plate 5. as to appear dangerous to thofe that walk at o* near its Foot, and 
Fig- 3. don't know upon what Principle it is fafe. 

%gr.*5. 43. If HI ^ the lower Part of the Body abed* be equal, fimilar, 
Fig, ^1 and alike inclined, to the Body ABED, it will not fall for the Rea- 
fcn above-mentioned, its Center of Gravity being then at but 
as foon as the upper Part or Cylinder ^ £ IH is fet upon it, and 
made faft by the Pins ff> it brings up the common Center of Gra- 
vity to c r and then the two (which are now become one Body) 
fall towards 0 ; but if HI ed being held faft 3 the upper Part ab H I 
be fet upon it, that Part will ftand fall without the Help of the 
Pins ff\ for as its Center of Gravity is at G, its Line of Dire£H* 
on will go thro* the Plane HI which is now the Bafe of the Body 
ab IH. But upon letting go Hied, the upper Part will bring 
down the lower, and they will fall together, beginning to move 
round the Center of Motion e, the common Center of Gravity c 
^ difcending, towards i*. 

E X F E RIMENT XIII. 'PL Fig. 4* 

*- Pi. 5; 44. If in the Hand H* be held upright a Needle or fharp point- 
Fi s- 4; ed Broach as C> the Fork D, whofe Center of Gravity is at D, be- 
* * n g fet u P Gn Point of this Needle will be fupported *, though it 

will be difficult to place it right ; becaufe the Point of the Nejedle 
is fo fmall a Bafe, that it will require a nice Hand to bring the Cen- 
ter of Gravity fo directly over that Bafe as to make the Line of 
^ Ann. 1 5, Direftion go thro* it*. But if another Fork, a* B, f be ftuck into 
the Handle of the fir ft, and a third of equal Weight with the fe- 
eond, as A, be ftuck upon the Points of the firft,, all the three wilt 
be fuftairied. 

The Line AB> which goes thro 7 the Centers of Gravity of the 
Forks A and B, being biffb£te$ at c r fhews that Point to be the 
common Center of Gravity pf thofe two Bodies : The Addition of 
39. the Fork D alters the Center of Gravity*, and caufes the Point C 
( which is as near again to a as to D, the Center of Gravity of D) 
B> to become the common Center of Gravity of the three Bodies 

In this cafe the Bodies will be all fuftained by means of the Needle: 
under D, becaufe the Center of Gravity is as low as it can be : On- 
ly with this Difference ; that in the Cafe of the fingl^ Fork the 
Center of Gravity (which was then over the Center of Motion) 

wou'dl 




wou'd defcend upon the leaft Shake, and throw down the Fork ;Le£fc. II. 
but now no Shake, but what is ftrong enough to make D jump off s-/"*Vs- 
from the Point of the Needle, can caufe the Bodies to fall, for if 
the Center of Gravity be rais'd out of its Place, it will always re- 
turn to C the loweft Point it can defcend to *. ■ * a* 

45* Since the Line of Direction runs through the fupported 
Point under D, it follows, That a Body-j or Syftem of Bodies will 
be fujiained (that is,their common Center of Gravity wonYdefcend) 
when any "Part of the Body which is in the Line of 'Direction is 
fupported s but will fall when no 7 art which is in the faid Line is 
fupported. 

46* If by a Force imprefs'd upon the- Bodies A or B *, or both,* pi. ,5, 
they be made to turn round each other and round the Center r, Fi g- 4« 
in a Circle whofe Diameter is AB; they will ftill be fupported as 
before ; whether they turn faft or flowly round *; and whether D* 3*» 
be heavy or not, in which latter cafe the common Center of Gra- 
vity will return to c\ and whether D, C, or** be the Point fupport- 
ed : Nay, if the Hand that carries the Bodies ftands ftill, or moves 
in a right or a curve Line, the fame will hold ; that is, the A&ion 
of the Bodies upon each other (or in refpe£t to each other) will 
not be alterM thb 7 they are carried along with their Center of Gra- 
vity : Neither will the Alteration of the Plane in which the Bodies 
move ( that is here the rifing of A and finking of B, or the riling 
of B and finking of A (as they turn) have any Effeft upon the Mo- 
tion of their Center of Gravity • Thus whether the Moon and 
Earth move faft or flow about each other, and their common 
Center of Gravity ; and whether the Plane of the Moon's Orbit 
be more or lefs inclinM to the Plane of the Ecliptick, and whatever 
may be the Change of that Inclination, the Motion of their com- 
mon Center of Gravity (which defcribes the Magnus Orhis) will 
be no way affected. 

Ex? e r 1 m e k t XIV. TL 5. Fig* 5. 

47. If fuch a Body as AB* befet upon the Pedeftal NDP,it will fall, * pl - 5- 
becaufe its Center of Gravity can defcend (in the Arc C q) or, which Flg ' 5 * 
is all one, no part of it that is in its Line of Dire&ion CO is fupport- 
ed ; but if the two Awls L,M, be ftuck into the faid Body, their com- 
mon Center of Gravity being at k (in the Mid- way between L and 
M) will bring back the common Center of Gravity of all the three 

I 2 Bodies 




A Courfe of Experimental PhUo/bphy, 

Left, II. Bodies to K, and then K o will become the line of Dife&ion of 
ory^w the Bodies, in which the Point K being fupported the Bodies can- 

* 45 ; not fall 

♦Plate j. 48. Likewise the Body AB * being fet upon the Pedeflal AE 
"V- 6 - would fell, its Center of Gravity moving round the Point M in 
the Arc C q. But if an heavy Body, as D, be join'd to it fo as to 
bring the. Ceriter of Gravity to K, then CO will ceafe to be the 
Line of Dire&ion ; and in the Motion of the Bodies round M the 
Center of Motion K muft defcribe the Ark K k moving upwards,, 
■* 24* which cannot be therefore AB will be fupported by adding an« 
other heavy Body to it. 

49. When Bodies are laid upon an inclra'd Plane, they will 
come down, though the Line of Direction tails within their Bafe* 
In fuch a Cafe their Center of Gravity will not move in their 
Line of Direction (which only happens \vhen Bodies fall freely) but 
will move in a Line parallel to the Plane, the Body Aiding all the 
while. But if the Line of Direction of the Body falls out of its 
Bafe, which is applied to the Plane, the Body will tumble or roll 

* Ann. x|. along the Plane *♦ 

Experiment XVI. TL 5. Fig.j. 

^ Hence follows that the fame Body, that in one Pofition wou'd 
Aide along an inclined Plane, will roll down in another. Thus the 
opiate p Body ABCD % when fet upon the Plane fMN, will Aide in the 
Kg. 7. Pofition abed, becaufe its Center of Gravity k cannot fall in the 
Line of Dire&ion of ko ( the Body being ftoppM by the Plane) 
nor move in the Arc kc about d for a Center of Motion; becaufe 
in this laft Cafe the Center of Gravity muft rife, which cannot be* : 
And therefore the Center of Gravity will defcend in the Line 
k s. But if the fame Body fliou'd be laid on in the Pofition 
abed, itwou'd tumble towards M, its Center of Gravity de- 
Iceriding in the Arc K^. For this Reafon a Column may be 
drawn up aa Hill when laid along in a Waggon, which wou 7 d 
tumble backwards if fet upright in the fame Waggon: And a 
Load of Hay wou'd be overthrown going along the fide of aa 
where the fanjg Waggon would go along fafely, if loaded 



A Courfe of Experimental Philojhphy. 6 r 

with an equal "Weight of Iron ; only becaufe in the Load of Iron Le£t. ■ IT. 
the Center of Gravity is low ; but very high in the Load of Hay^.L^WJ 
What has been fa id in the three lafl Paragraphs * will be farther * Ann * 1 7- 
confirmed bv the following Experiments. 

Experiment XVII. ?/.5< %8. 

jo. Upon the Table Tt T * which has a' S lit from X to x, fet the * Plate ^ -.. 
little Image DM in fuch manner that the Saw c (which is faften'd Fi S- 8 - 
at one end to the Hands of the Image, and has a Weight W fix'd 
at the other end ) may pafs through the Slit X x, ^and the Image 
will ftand in an upright Pofture : Then if the Head of the Image 
be brought down to A or B, it will imitate the Motion of Saw- 
ing, and vibrate feveral times in the Arc A o B whilft the Weight 
W does in the fame manner defcribe the Arc VWV, the Center 
of Motion of the whole (that is, of the Image, Saw, and Weight) 
being at M; the common Center of Gravity K does likewife de- 
fcribe the Arc LKL, till (after having feveral times defcended from 
L on either fide) it comes to fettle at K, juft under the Center of 
Motion. If the Image had no Saw, it would ftand upright when fet 
on the Table, becaufe its Center of Gravity C would then be 
iuft over the Center of Motion M* ; and fome Part of the T* 2 ^ 
mage which is in the Line of Direction o O would be fupported *, * 45 ' 
but the leaft Alteration of Pofition that fhould move c from 
over M would throw down the Image *. Then if the Saw c be * , 
added ; fince its Center of Gravity is at c, the common Center 
of Gravity of the Man and Saw will be at L, and in that Cafe 
the Image with its Saw will fall towards X; but if by means of 
a curv'd Wire the heavy Weight W be join'd to the Saw ; the 
common Center of Gravity of the Man, Saw, and Weight, will 
be atK*, and the Line of Direction will again be o Oj therefore the * 5 gv 
Image will ftand in its upright Pofition. If now the Image be 
inclin'd forwards or backwards, it will after feveral Vibrations re- 
turn to its firft Pofition, becaufe the Center of Gravity always en- 
deavours to defcend to K, in doing which it will bring the Image 
upright. N. B. This Experiment fucceeds heft with two littler 
joints in the Heels of the Shoes to hear on the Table, 



E x F -E E I— 



% A Coitrfe of E^primental Philofophy 

Left* 

v, ^ viN ^ Experiment XVIII. PX 5. Fig^S. 

■* p] S 1 ' ^ PON the Stick Si 1 * (which of it felf would fall from the 

Fig/s! 5 ° Table, becaufe its Center of Gravity hangs over) fufpend the Pail 
P, fixing another Stick pq, one end in a Notch at /, and the o- 
ther againft the infide of the Pail clofe to the Bottom, and the 
Pail without: any other Help will be fupported on the Stick S s 9 
which will not fall from the Table though the Pail be afterwards 
filled full' of Water, provided the Bale or Handle of the Pail be 
pretty near the Table, and the Stick pq long enough to pufh the 
Pail a little out of the upright.' 
* Plate 5. When the Stick SS *is horizontal on the Table TWB, c is the 
FJg. p. common Center of (Gravity of the two Sticks SS PQ, the Paii 
DQE, and the Water eontain'd in it, all which taken together are 
to be look'd upon as one Body whole Line of Direction is 00; 
and as the part of SS which is a little behind the Bale B is in the 
Line of Diredion, and fuftain'd upon the Edge of the Table, the 
whole Body abovemention'd cannot fall ; for if it did, the part 
BS muft rife at the End S, into the Pofition B jy and PS defcend 
into the Pofition p s r which cannot happen unlefs the Pail rifes in- 
to the Pofition dqe bringing up the common Center of Gravity 
■% toe in the Arc C e D, which is impoflible * from Gravity alone, 

without the Aftion of an extrinfecal Agent. But if the Pail DE 
be lifted up under the Table, and the Stick SS inclined above it, 
fo that the whole Machine comes into the Pofition ss pe q d : 
If then it be left to it ftlE, and the Stick ss is fo fmooth as well as 
the Table under B that there is little or no Fri&ion between them, 
the whole Machine will Aide down and fo fall from the Table ; 
s s moving in the Dire&ion sps y and tbe common Center of 
Gravity c in the Line e E Tangent to the Arc D c C. Here it is 
obiervabie that as 0 0 is now the Liner of Dire&ion, no Part of 

the BaHy-kVtbe.feiy Linp fypported ^ 
N. B* The Experiment is 



Annotations upon the Second Lecture, 



i* C 3* ,l — ~ By in Velocity.*} 

OME Authors have confounded Velocity with Motion tho ? it is Antiotat- 
but an Adjunct of ft, imagining that one Body muft have as niuehLell. M 
Motion as another, whenever it moves as fall, and more Motion W^V^W 
when it moves fafter^ but this is only true when the Bodies have equal 
Quantities of Matter, or when we compare the Motion which a Body has 
at one time with the Motion that it has at another. ;; The general Defini- 
tion indeed (viz. that Motion is the Tranjlation of a Body from one Place to- 
mother) takes no Notice of the Quantity of Matter ; but when we compare 
moving Bodies, we have a Regard to their Quantity of Matter, for Velo- 
city alone, without confidering how much Matter is mov'd, will never enable 
us to determine the Force, which we call the Quantity of Motion. For 
example, Ihou'd a Dog and an Horle moving with ecjual Swiftnefs run againfit 
a Wall of the Thicknefs of a fingle Brick-, the Dog wou'd be beaten back^ 
whilft the Horle that carried 40 times more Matter woud beat down the 

Wall, &e> 

2 . [j. ■ t ■ ■ Force cmd Motion mean the fame tfhing.'] See Sir Ifaac New~~ 
ion in the Beginning of the firft Book of his Principia , Def. 2. and 8, 

3. . Left Matter than the Ram.'] If the Battering Ram R * * PL 4, 

fee 28 Inches in Diameter, and 180 Foot long, made of feyerai Pieces of Fig* 2, 
Timber, as for example, of Oak jpyn'd together, it will contain^o Cu* 

bic Feet of that Timber,, which at 50 Pound a Cubic Foot will weigh 
37500 Pounds: If the Head of it made of Caft Iron weighs a Ton and a 
half, that will be 33 60 Pounds , then if the five Iron Hoops* about it are one 
Inch thick, two Inches deep and 94Tnehes in Circumference, they will weigh 
about 50 Pound each, which with two Pbundsof Nails allowed to keep them 
tight to their Places will make 252 Pounds : Now all thele Weights added 
together will give us 411 12 Pounds for the whole Weight of the Ram >; 
which if it oe mov'd by 1000 Men employed only to make it ftrike againffc: 
the Point L of the Wall AHIGE (fuppofing it to fwing fulpended by its 
Center of Gravity from a moveable Gallery or only a Treffel) each Man 1 :, 
will move a Weight of 41 Pbunds. The Quantity of Motion produc'd by, 
this Affion, when the Ram moves one Foot in a fecond, may beexprefs'cfc 
fey the Number- 41 1 1 2 ^ which* Motion or Force, compared with the Quan* 





Courje of Experimental PMIofophy. 

Annotat tity of -Motion in the Iron Bail B fhot out of the Cation C, will be found 
•ULea. IL equal to it: For a Cannon Ball is known to move as faft as Sonnd for the 
U^VNJ Space of above a Mile, and if you multiply 36 Pound the Weight of the 
Ball by 1 142 (the Number of Feet which Sound moves in one Second ) you 
will have the Number 41 1 1 2 to exprefs the Force or Quantity of Motion in 
the Ball B ftriking at L. And if, after a few Strokes given by the Batter- 
ing Rarii, the Mortar or Cement is fo loofen'd that the Piece of Wall 
ADDFE is at laft by a Stroke of the Ram carried forward from F to K 
and fo beaten down j the lame thing will be performed by one Cannon 
Ball after the fame Number of equal Strokes given before by others, as we 
had fuppofed by the Battering Ram 3 and then the Quantity of Motion in 
the Piece of Wall ADDFE carried from F to K will be juft equal to the 
Shock of the Ram, or of the Bullet B. 

This fliews how advantageous the Invention of Gun-powder is 5 fince we 
are thereby enabled to give fuch a prodigious Velocity to a fmalJ Body that 
it fhall have as great a Quantity of Motion as a Body immenfely greater 
and therefore perform as much by its Percuffion tho' we ufe but tew Hands 
in the Management of it, for three Men are able to manage a Cannon' which 
fliall do as much Execution as the Battering Ram abovemencion U Thofi 
that would have a more ample Account the Battering Rams and warlike- Ma* 
• chines of the Ancients may find them defer m in fever al Authors, officially in 
^ohorch. Juftus . Lipfuis * the Ram which I have confidered here is taken at a Mean 
1 3" hing bigger than fome and lefs than others that we read of 7 

4, £ rii — —Subtiie Matter, &c] The Cart eft ans, in order to maintain 
their Plenum, fiippofe a certain fubtle Matter to fill all Spaces between 
and Pores within Bodies, and that this fubtle Matter by being continually 
divided, becomes fo fine a Duft as to have neither Weight nor Refiftance, 
and yet that it is the Caufe of Gravity 5 but any one that conliders. this at 
fertion will find it inconfiftent with itfelf. For firft if fuch a Matter filPd 
all the Interftices between the Parts of Bodies, it wou'd render them equally 
full: Secondly, Wherever it fiil'd any Space that had no other Bodies 'in it, 
it mud be more folid than Gold and harder than Diamonds, and confequent- 
ly could not be a fine Duft as is imaging for a Body, when fo!id 5 differs 
from the fame Body in Duft, only becaufe its Parts arefeparated irorn'one'an- 
other, fo as to have a great many Voids between : As a Pound of folid 
Gold differs from as much Gold Duft, only becaufe the Parts of the Duft 
are more feparated, mix'd with Vacuities, and do not touch in fo many Points 
as the folid Lump ^ the Duft eafily becoming a folid Lump when the Vacui- 
ties are driven away by Fire, which turns the Duft into a Fluid that after-, 
wards (upon the Removal of the Fire) is chang'd into a folid Lump with- 
out lofing any of its Weight, thirdly, As the Gartefians affirm — That of 
fuhtile Matter the Earth and Air ( heavy Bodies ) are compounded, it is 
abfu . d to fuppofe the Matter of which they are made to be without Weight % 
fince the Gravity of any whole Body is made up of the Gravity of all its 
Pans, taken together. Fourthly, When the Cartefians make their fhbtile 

Matter 



A Courfe of Experimental Pbilojophy. 



6$ 



Matter the Caufe of Gravity, they feem to forget what they have laid of it Annotat. 
before, namely, that it has no Refiftance ; for i f a Fluid, by its Motion about the Left IL 
Earth, impells all the Bodies near it to fall down to the Earth, it cannot be void s^v^j 
of Refiftance, becaufQ whatever impells xnuft reftfi : And to fay, that folid Bo- 
dies can move thro' this fubtile Matter without fuffering any Refiftance, but 
that the fubtile Matter when it runs againft folid Bodies drives them 
out of their Places, is an Abfurdity unworthy of a Philofopher. Yet be- 
caufe the Carte/tans cannot deny the Experiment of a Piece of Gold, and a 
Feather falling equally faft in a Glafs Receiver out of which the Air has 
been pump'd* (and the Experiment has been made in a Receiver 10 Foot* 1,7 1. 8. j. 
high ; fee Phil Tranf No. 35.4) rathter than give up their Plenum, they lay, 
that when the Air is pump'd out, the Receiver is as full as before, but that 
it is fill'd with fuch a fubtile Matter as makes no manner of Refiftance : So 
that upon the whole, the Carte/tan Account of the Caufe of Gravity, and 
the Non-refiftance of their fubtile Matter, are inconfiftent with each other. 
Many more are the Contradictions which they fall into by endeavouring to folve 
Phenomena by the Powers and Motions in all Directions which they attri- 
bute to this fubtile Fluid; but I fhall "fay no more on this Subject, till I 
come to fpeak of the Motions of the heavenly Bodies. 

5. C \ 6. At once with the Leaver."] It was upon this Principle that Archi- 
medes propofed the lifting of the whole Earth, in caie that there could be 
found a fix' d Point, or Place to fupport his Inftrument, Sos ttS ?6 ; , ^ rov kowSv 
kivhVg). By which he meant — That the leaft Power, by encreafing its Velocity, 
might raife the greateft Weight j and that in this Refpeft there are no Bounds, 
where we can get a Place for a fix'd Point, and a due Diftance for the Pow- 
er. Now, tho' raifing the Earth is a Propofition purely Mathematical, and 
not to be reduc'd to Practice $ yet for Curiofity Sake we'll confider it a little 
here. 

If we take the common Center of Gravity of the Earth and Moon for 
the fix'd Point (Fulcrum, or propping Point) of our Leaver, which we will 
fiippofe 240000 Miles long, that is, reaching from the Center of the Earth 
to the Center of the Moon $ then the Moon, or a Weight equal to it made 
ufe of as a Power, will be able to fupport the Earth at the other End of the 
Leaver } and if it be removed but an Inch farther, it will raife it up. * Here * No 15. 
the Diftance of the Center of Gravity of the Earth from • the fix'd Point 
of the Leaver is <5ooo Miles, and that of the Center of Gravity of the 
Moon or Power is almoft 40 times as far 5 and if the Moon be fuppoled 
to move with the fame Velocity that it woifd fall to the Earth by the 
Force of Gravity, if its proje&ile Force did not hinder it j then the Earth 
would be moved one Inch out of its Place, by the Moon's moving about 
40 Inches. 

Now if, inftead of" the Moon, we make ufe of a Power whofe Intenfity is 
equal only to a Weight of 200 Pound, as for Example, the Force of a Man, 
as Archimedes propofes : Then ftill fuppofing the Earth at the Diftance of 
<5ooo Miles from the fix'd Point, that Brachhwi of the Leaver to which 



the 





A Courfe of 

Annotat. the Power is applied, muft be lejigfced lp the Proportion that the Weight 
Left. II, of the whole Earth bears to 200 W§ jght, J& this m& the End of the 
Leaver Will reach quite out ofwr Syften* among the fix'd Stars, above fifteen 
thoufand Millions or Millions of times farther ihm the Diftance of Saturn-: 
Md if Archimedes (or the Power) be ftppps'd to prels upon the Engine 
With the Velocity of a Cannon Ball, fie wmitt be in Motion at the End 
of the Leaver above 26 and near 27 Millions of Millions of Years to raife 
the Earth one Inch in that Time, and wou'd go thro' a Space above 39 
thoufand Millions of times greater than .the Periphery of Saturn's Orbit. 

For the Sake of fee b. as -wou'd examine this CalcuMion, ws fubjoin the Num- 
bers that we made ufeof. 

The mean Diameter of tfc Earth is equal to 19 688 72s Paris Feet 
{ Newton. Prine. Lib. 3, Prop. 2 e. /Vg. 387.) 

.Snppofing the Diameter to the Circumference as 7 to 22; and multiplying 
the Diameter by the Circumference, you will have 1 21B 315 660 966 250 
Square Feet for the Surface of the Earth : Which laft Number, multipli- 
ed by the fixth Part of the Diameter, will give 3 997 847 001 180 744 
£47 S97 i for the Cubic Feet contained in the whole Earth. 

Now if we fuppofe a Cubic Foot of Earth to weigh 100 Pound, mufc 
tiplying by 100 we lhall have the Weight of the whole Earth in Pounds, 
viz. 399784700118 074454789750. 

Then, As 200 Pound (or the Intenfity of the Power): 

Is to 399784 700 j 18 074464789750 (or the Intenfity of the Weight) : : 
So is 6000 Miles {the ■ Difianee of the Weight or of the Center of the Earth 
from the ft^d Point) : 
To 11 991 541 003 542 233 943 69% 50© Miles (or the Diftmee of the Power). 

This laft Number not only exprefles the Diftance of the Power, but the 
Number of Mile? that the Power muft move to raife the Earth one Miie^ 
became the Velocities of the Power apd Weight muft be reciprocally as their 
Malfes. But if we wou'd raife the Earth but one Inch, we muft divide by 
66 3 60 (the Number of Inches in a Mile) and we fhall have the Miles gone 
thro' by the Power whilft the Earth moves 1 Inch, viz. 189 291 906 «;8? 
668465020 Miles. ■ y> 3 5 

To have a clearer Idea of what has been faid, let us compare the Diftance 
of the Power and Space that it muft go, thro', with feme great Diftance 
that we know, and with the Space deicrib'd by fome Body that we can ob~ 
ierve } as for example, with the Diftance of the Planet Saturn, and the Space 
which it defcribes in going thro' the whole Circumference of its Orbit. 

Saturn, at its mean Diftance from the Earth (which is equal to its Di- 
ftance from the Sun) is above 9 times and a half (or 9,5 1 times) farther from 
the Sun than the Earth, which laft we fuppofe 8 1 Millioas of Miles from the 
Sunj and therefore will be exprefs'd by this Number of Miles (viz^ 

V °l\fu° 0i *L which dividin g 11 993 54i o°3 54* 233 943 692 «KT, 

w,e lhall .haye a Number which feews- us that the Power muft be applied 

farther 




fitftlier from the Fafchrtiirroif Center of Motion thetf Sdttirtfs Dirfance, AMtitM 
if $6$ 74 j 95 1 ojj 73 1 tfrftes. Then if the Spice that the Power muff go Left It* 
tM>' (or 189291 $83 &68 4&5 oio Mil& ) be divided by 4 841 948' j 71 : ' ' 
the Numbed of Miles in the Periphery of Saturti's Orbit, the Quotient will 
Ifcew us that Che Power will go thro' a Number of Miles 39 094 177 4*8 
times greater, ■ ■ ; 

Agaiby if we fuppofe the Power, or Archimedes puifci% forviftrd the faf theft 
End of the Leaver 5 we fhall findy that tho' he fiiould move as faft as 
a- Cannoft Ball, he wou'd fpend 26 978 123 942 4 £o Years in moving the 
Earth one Inch. For if we fuppofe a Cannon Ball to move With the fame 
Velocity as Sound, or a Mile in 4 Seconds and an half (as Experiments 
have confirm'd it) it muft move 800 Miles in an Hour : And as one Year 
contains P766 Hours, 800 times that Number is the Nuniber of Miles which 
a Bbdy with the Velocity of a Gannon Ball would move in a Year 5 by 
Which Number (j 012 800 ) if you divide 189 291 $96 583 66846*020 
I the Number of Miles that the Power goes thro') you will have the 
Numbet of Yelars whielv if muff take up erf go " thto' the' laid Spkc^ namely 
26 978123 94^2 "-4-6& Yell's, which was to be proved. 

; Bijh&p ■ Wilkins- m his m€(Mmc^ Powers rtietftiM a compound EngiM of 
Wheels , whereby'- tM Earth' migflt be rais } dy without fdppofing the Power 
M be applied at any confiderable Mflance from the Earth; but what tie 
fay? depends • mfrety ! ; ; upOn' the ' ftm Principe \ for even in that Cafe y ib% 
Power ( if epal to what We hme fuppos'd) muft go through a Length e- 
qual W Os many Miles as we have- mention* d above, in order id rat ft the Earth 
but one Inch \ though the Line : in ^ which it tnorfd JhdUld be but d Circle of a 
Foot in BtameUry fof r WfhfrMMhiM be 'Made : inatif rhdhrier ^h at every the 
Different of the Velocities of the Power and Weight will always be recipro- 
cally as their Maffes (of their Intenftties') eonfidering the Power as a Quantify 
of Matter in Motioti) when they balance one another , and the Jmalle ft Addition 
of Velocity (fill fuppos'd in theft Calculations) will make the Power oveipoife* 

6. \^ 16. —Where we Would gain Tim we muft employ more Strength."] For 
want of rightly confidering this, agreat deal of Time and Money has beeti 
fruidefsly Ipent in mechanical Works, by fuch as imagine that Force might 
be generated by the Figure of a Maehlne ^ whereas Mechanics teaches 
riot to make, but to apply Powers, fuch as we find them in Nature > for 
We deceive our felves> if we think that by means of any Engine whatever, 
One Man fHali do the Work of Two in the lame Time, firppofing the Men 
to employ the lame Strength. But yet the Science of . Mechanics is not to 
be rejeded as ufeieis y for to the pra&ieal Arts that are deriv'd from that 
Science we are indebted for a great many of the Neceffiries as Well as Colli 
venienCies of Lifei In the Performance of leveral Works, where we have 4 
fufficierit Strength y we- often want Time v atxl fomefcimes where we have 
Time to fpare we want Strength, In fuch Cafes the Skill of a good Me- 
ehimicMs to^be exerted jri^direaing the Application of the Powers accord- 
ing to-Time. Thus in making Harbours, and carrying on Digues, Moles 1 

K z or 



68 A Courfe of Experimental Pbtfofophy. 

Annotate or Banks, where at every Tide the Sea may damage the Work, and a 
Left. IX. Spring-Tide over- fet its the greateft Number of Hands muft be employed 
KJ^TSJ that can work by one another. In fome Cafes, as raifing Blocks of Marble 
or other heavy Goods out of Ships to lay them upon a Wharf, many 
Hands cannot be employ 'd ^ either becaule they cannot well ftand by one an- 
other about the fame Block-, or becaule they cannot lift all at once $ or 
when they have got up their Burthen, they cannot conveniently walk with 
It } or if they could, the Planks over which they go, or Ladders which they 
muft climb, could not fupport them and the Weight $ then an Engine muft 
be us'd (as for Example, a Crane) where one Man fliall do the Work of 
io or 20 Men, but he fhall be 10 or 20 times longer in performing it. Yet 
the Engine is abfolutely neceffary % becaule without it the Work could not 
be done, therefore a Efficient Time muft be employed, without which a 
great Strength would be of no Ufe. Thus likewife in Building we muft ufe 
Engines to raife great Stones and large Pieces of Timber, where fo much 
more Time is employed according as the Force of the Men working at the 
Engine is lefs than the Force that would be required to raife the Stone if 
the Hands were applied direftly to it \ but then the Engine takes up lefs 
room, and the reft of the Men may be otherwile employ 'd. In draining 
Mines we are always confined in Time, becaule the lubterraneous Springs 
fupply the Water whilft a Force is employ'd to draw it out ) and in fuch a 
Caie the Power (that is, the Intenfity of it ) muft be fupe rior to the Qiianti- 
ty of Water to be rais'd in a certain Time $ that is, the Power muft be a- 
ble, without any Engine, to draw from the Bottom to the Top of the Pit 
(fuppofe an Horfe drawing up a Bucket faften'd to a Rope that runs over 
a fingle Roller ) a Weight greater than the Weight of the Quantity of Wa- 
ter that runs in, during the Time that the Power goes through a Space e- 
qual to the Depth of the Pit. Engines are applied for the Conveniency of 
delivering the Water, and not to gain any Degree of Force } for we always 

lofe fome So much as is employ 'd to move the Parts of the Engine^ 

which cannot be apply 'd to one another without a Friftion that fpends 
fome of the Power*, fo that the beft Engine is that which confifts of the 
feweft Parts And he that by Machinery pretends to gain by bringing 
up a greater Weight, or a larger VefTel of Water with the fame Power, 
does not confider, that it will rife fb much the flower, and give Time to 
the Springs to fupply more Water in Proportion; or if, by adding any Part 
to the Engine, the Power (as for Example, an Horfe or Horles) is made 
to go eafier, then lefs Water will be rais'd at a Time. Thh Jhou'd give a 
caution to thole that have any Concerns in Mines, Water-works, Mills, or 
other Manufaftures *, that they might not be impos'd upon by Engme-makers 
that pretend to (and often fancy they can) by fome new invented Engine 
out;do all others, and make one Horfe do as much as three or foun 
This proceeds from their being unskilled in Mechanical Principles^ the 

* All that relates to r&$ng Water fijill be particularly con§M£i^ when we come to heat of By* 

Know* 



A Courje of Experimental Thilqfophy* 6$ 



Knowledge of which Would- keep them from attempting ImpoffibilitieSc It Annotate- 
were to be wiih'd that our Engine-makers, who often abound with Inven- Lett* XL 
tion^ and are generally quite ignorant of Mathematics, wou'd apply them- Kj^Ts) 
felves to that Science ^ at leaft to know lb much as wou'd dire£fc them in 
their Works 5 or that fome of our beft Mathematicians wou'd not think it 
below them to dire£t Workmen, and confider Engines a little more than 
they do, which wou'd render their Speculations more ufeful to Mankinds 
There are forae, who, being too clumiy, and wanting a nice Hand to 
make Experiments, are unwilling to own it, and therefore ridicule and de~ 
fpife Mechanical Performances } forgetting that the incomparable Sir Ifaac 
NewtoriyWhom They with all other Philolbphers admire, has made as many as 
(if not more Experiments than) any Man living 3 and look'd upon Geometry 
as no farther ufeful than as it directs us how to make Experiments and .t" 
Obfervations, and draw Confequences from them when made , fo that the 
Improvement of Philofophy muft be the Refiilt of mix'd Mathematics, that 
is, of Mechanics and Geometry. A Man that fhou'd learn to fence by 
Book, wou'd. be as much at a Lois if he was caliM to fight, as another that 
fhou'd prefer brutal Courage to the whole Art of Fencing} only with this 
Difference, that the latter wou'd be much more likely to kill his Adverfary^ 
as Men quite illiterate have often produc'd wonderful Engines. The Ma- 
chine at Marly which was made by an ordinary Man of Liege, who was en- 
tirely ignorant in Mathematics, has a great many excellent Contrivances y 
but does not raife all the Water that it fhou'd do, becaufe the Workman 
did not know how to calculate, fo as to give the Fbwer of the River Seine 
its utmoft Advantage. 

When great Works or Manufactures are carried on in fuch a Manner that 
a great Part of the Intenfity of the Power is ulelefly fpent, and but little 
of it employ'd in doing real Services y as for Example, when there are un- 
neceffary Frictions arifing from the ill Contrivance of the whole Engine or 
the wrong Figure of fome of its Parts, or the bad Performance of the' 
Workman } or if Men or Horfes, &c. exert but a fmall part of that Strength 
which they might apply without Wearinefs or Inconveniency : Then the. 
Skill of a good Engineer may be advantageoufly applied in changing the; 
Form or altering, the Parts and Motions of a Machine. An Inftance of 
this may be leen in the winding of Thread or Silk, in which Bufinefs if 
50 Men being employ'd they fhould only move a Weight or overcome a 
Refiftance equal to half a Pound, as they carry their Hand round (where- 
as one Man can eafily raife 25 Pound, with the fame Velocity as his Hand 
moves during the Space of 10 Hours in a Day ) a Machine may be con- 
triv'd whereby one. Man applying his whole Strength fhall do the Work of 
the fifty Men in the' fame Time. Thus in any other Cafe Machines may 
afford ns great Profit, by rendering effectual that Force or Intenfity of the 
Power, or Powers, which was before milapply'd or not employ'd at all 
This has been perform'd at Derby in a very ingenious Manner by Meffieurs 
Thomas ' a d John Lombe, who have employ'd the Force of a- Water-wheel 
to the. working; of Italian Silk}, fo as to loie or mifpend no Part of the 
Power, -As** 



Annqtstt* 
HLe£t. II, 



* Polior e 
Lib. 3. 
Dial A 4. 

t PI- U 



* PL 6. 



g. 1. 



A$:tbe Proprietors of this curious Machine are not willing to have a De- 
ftription of the whole Engine or any of the Movements of it made Puli- 
lick, I ihall only here give the general Account of it^ viz. That there are 

26 586 Wheels. 
#7.746 'Movements. 

73 728 Yards of Silk wound every time the Wheel goes round^ which 
is three ' times ' every 1 Minute 9 

3 18 5 04 960 Yards of Silk in one Day and Night 7 and consequently 
99311 547 5 5° Yards of Silk in one Year. 

One Water-wheel communicates Motion, to all the reft of the Wheels and 
Movement S) of which any one may be flopped feparately and independent on the 
reft. One Fire- Engine conveys Air to every individual Fart of the Machine^ 
md om Regulator governs the whole Work. 

7? C 1 7 — ■ Scorpions ) &c . give afujftcient Velocity, &c. j Scorpions were Ma- 
chines to throw 'Arrows, Fire-Balls, or great Stones. A Defcription of 
them may be found in Vitruvius and the above-mention'd Lipftus from whom 
I have taken the Figures reprefented in Plate <5. The ift Figure re- 
prefents one of thefe Machines charged. The Point A of the longefl: Bra- 
chium AC, vvhich in the natural Situation is kept uppermoft by the Boxes 
of Stones or Weights BB, having been brought down to A (by the Rope 
RR and Loop % drawn by Help of the Wheel W and Pinion at I round 
the Rollers M and L) is kept from riling up again by the Pin HH, made 
a little taper : Then the Loop a being taken off - from Ay and the Sling S 
being chargM with the Ball or Stone T, the Scorpion is ready to be di& 
charg'd v which is done by a fmart Blow of an Hammer on the End H * 
of the Pin, or a fudden drawing it out with a Rope, for then A being, no 
longer kept down .-riles with great Velocity by the Defcent of the Weights 
fiB,. and one of the Loops of the Sling flipping, off of the Point A 7 made 
conical for that Purpole, the Stone flies out as reprefented in the fecond Fi- 
gure, which is another Scorpion little differing, from the former. AHithe 
Uiflference is, that in this laft Figure, as the diftharging End A is the Axis 
of Motion DD, then the fame End in the former Figure, the Pulley * 
L is ; applied in fuch a Manner as to caufethe Handle I of the Pinion lead- 
ing the Wheel W, to move as ealy again as in the former Cale: And as to 
the Effe% fuppoling th$. Weights Bf^ equal in both Scorpions - 7 the latter 
will throw a Ball of greater Weight, but then it will have leis Velocity than 
the former Proje&ile. In both Cafes the Scorpion turns upon the Pivot 
C, and the whole Frame HI round the' upright Shaft Cc r that the Machine 
may be v directed any Way. The. . Hook-Baa- the fecond >: Figure does the 
Office of the Pin H in the firfh , 

However powerful thefe -Machines were, and however numerous* they ;ane 
not to be cQmpared with a Battery <of Cannon, either for Force or Jfixpecli* 
*W% .-.BifliQp- Wilhins had not preferred them ; to our Artillery , as feme o«. 



ji Cmfft of ExperimMal PUiqfiphy. 71 

tfcmt-fc&w imty if he had examJifd iter* k& %^rficially, and calculated Atittotafc 
thekForce. # Lea IL 

To prove tbis r m will here conftdcr the Force of one of thete Scorpions, w'^V*** 
even fuppofing it much larger than oou'd conveniently be carried about (for, 
that they were probable, appears from the Account that Cafar had great 
..Numbers of them in his Camp) and we ftiall lee how much ihort it will fail 
of the Force of a Cannon. 

Let * AD the Tail of the Scorpion, or the End that throws the Stone * PL & 
or Bullet, be fnppofed 24 Foot long:, and the fhorter Brachia DB which Fi S- Iv 
carry the Boxes BB, 8 Foot long each. When the Boxes are fill'd with 
Stones (6 as to weigh, for example, tooo Pound each, and the Tail brought 
down to A in order to throw the Stone the utmoft Velocity that can 
be given to it can never exceed 48 Feet in a Second, becaule the Weights^ 
at B cannot fail fafter than 16 Feet in a Second, tho' they ihoifd not move 
the Machine jn their Defeent/, but as we may reasonably fnppofe that 
throwing up the Knd A loaded with the Projectile T, mult retard them one 
half, it will follow that the Body T will be thrown forward only at the Rate 
of 24 Feet in a Second, which is about 48 times flower than the Motion of a 
Cannon Ball \ and therefore the Effe£i of the Scorpion will be 48 times lels than; 
that of a Cannon throwing a Ball of the fame Weight. Befides, there rnnft be 
more Men to manage the Machine, and a great deal more Time fpent in draw- 
ing down A by means of the Wheel W, than in charging a Cannon - 0 for if we 
fuppole the Force requir'd to raifethe Boxes loaded with Stones, and to over- 
come the PVi&ion, to be equal only to 2500 Pound, and the Engineer who* 
turns the Handle at I to move his Hand thro' a Space of 3 \ Feet in a Second 
(which is the utmoft he can do if the Force he applies be equal to 25 
Pounds, he muft fpend 7, 6 Minutes, or above •§ of an Hour to carry the 
Handle thro' a Space of 1600 F'eet, in order to raife the Boxes 16 Feet in 
Heighth: This, befides the Time fpent to put in the Pin H and to fit the 
Stone T into the Sling S, will lb retard the Operation, that the Scorpion 
cannot difcharge its Proje&iie above 4 times in an Hour, whereas a Cannon^ 
may be -fir'd with great Fafe twice as many times in an Hour. 

Now if we confider how much fuch a Scorpion as we have defcrib'd mult 
weigh, it will appear as troublefome to carry as a Cannon. The upright 
Shaft C muft be^o Foot long:, an d that it may have fufficient Strength, we 
will fuppole it of ij| Inches in Diameter, which will make it contain 50 cu- 
hie Feet of Timber, which if of Oak will weigh about $0 Pound a Foot 3, 
let the Body and Tail of the Scorpion ABB with the Boxes BB, contain 
40 Foot more of the fame Timber \ the Frame &H 00 Foot, and the Whee£ 
W with the Pinion on the Handle I, the Pullies, Ropes arid Iron-work of 
the Machine weigh as much as 60 cubic Feet more of Oak : All this toge- 
ther will make 90 cubic Feet, which multiplied by 50 Pound will give 4500 
Pound, a Weight which will render the Machine very inconvenient, even 
tho' it be taken to Pieces. We may therefore fuppole the Scorpions much: 
lefs than what I have defcrib'd : So that there can be no Companion be- 
tween their EfMfc and that of our Artillery, WJaoever will be at the Pain^ 



72 A ' Courfe of Experimental Thilofopty. 

Annotat of calculating the Force of any other of the Machines nfed by the Ancients, 
Left, IX will find that they fall very ihort of the Effefts of Gunpowder : Elpecially if 
$**~V~SJ we confider what Force it exerts in the ipringing of a Mine, whereby pro- 
digious Rocks are rent in Pieces, and fuch Quantities of Earth and ftrong 
Walls lifted up, that all the Machines made ufe of in a Roman Army, if 
they cou'd be apply'd at once to one Part of a Fortification,, wou'd pro* 
duce nothing like this new Invention of a portable Powder which contains 
fuch an immenfe Force in fo Imall a Compafs* 

p , 8. C^r.- — Line of Direction, &c. endeavours to aft.*} Though an heavy 

jg/.^ Body as A # , may 'by a Force or Forces imprefs'd upon it, be made to 
move in any Direffion, yet (as it always retains its Tendency towards the 
Center of the Earth, which, ifnoObftacle hinder'd, would carry it the neareft 
Way) its naturalising ofDireffion always goes thro 7 the Center of the Earth 9 
and if, whilft the Body is going down by its own Gravity, it be hindered 
by one or more inclined Planes, as BG 7 BD^ and carried down afterwards 
in a Curve (46) in its Defcent on account of the Alteration of the Direc- 
tion of its Motion, or carried up again along another Plane as DE > we 
are not to call the Line 12346, or 12345 which it defcribes^ its Line 
of Direction; but when the Body comes from the Point 1 fuccefTively to 
the Points 2, ?, 4, its Lines of Direffion are 1 c, 2 c, 5 c , 4^, which are all 
directed to the Center of the Earth, and by reaibn of their great Diftance 
from it, may be confider'd as parallel, or indeed as one and the fame 
Line. 

^ Now the Line of Direffion of a Power varies according to the Applica- 
tion of the Power, whatever Line the Body a&ed upon moves in. Thus 
pl 7« when the heavy Body A* (whofe Line of Direction is ^C) fufpended by a 
«• 2 - Rope, is held by the Hand at H, the Line of Direffion of the Power is 
the fame with that of the Weight; but if the Rope be brought over the 
Pulley B, the Lines of Direffion of the Power may be any of the Lines 
BG, BF, BE, BD, whilft the Line of Direffion of the Weight ftiil con- 
Pi 7o tinues the fame. Nay, if the Body A *, being afted upon by the Power at 
Sg. 3. I, be made to move in the Line cD y along the Plane "MB, is not the 
Direffion of the Power but AL And if the feid Body be railed' from E 
to F by means of the Wedge KFL drawn under it (whilft a Board or im- 
moveable Plane at HG keeps it from going out of the Line EF) the .Line of 
Direffion of the Power will be LB: But if the Body having been plac'd at 
K upon the horizontal Plane L, the Wedge or inclin'd Plane F be fuppos'd 
immoveable, and the Plane HG to move from K to G, and to pufh up the 
Body in the Line KG, then does the Power affing in the Line of Direffi- 
on KG caufe the heavy Body to rife the Height EF, whether it moves in 
the Line KG or direffiy up in the Line EF to get that Height. 

Hence it follows that the Velocity of a Power is not to be confider'd in 
the iame manner as the Velocity of a Weight (unlefs when a Power at 
cends or defcends directly from or towards the Center of the Earth) for 
the Velocity of a Power is the Space that it goes through in a certain 'Time, 

which 



A Courfe of Experimental Philofiphy. 

which may be greater or lels to perform the fame Operation, according to Annotac." 
the manner in which it is applied; as the Power B* moves only the Left. II. 
Length LK, when it raifes the Weight up through the Line EF, by draw v u^V" 
ing the Wedge LFK through EF:, but if it pufhes it up along FK fup-* Plate7 ' 
pos'd immoveable, it muft move the whole Length of the Diagonal FK of lg ' ^ 
the Triangle LFK. But whether the Weight rifes from K or from E to 
the Point F, its Velocity muft only be call'd EF, becaufe whatever Line 
it runs thro', it only rifes (or removes farther from the Center of the Earth 
the Height EF- So likewife the Velocity of A * is only the Line i c 7 when * Plate 7, 
the Body runs thro' a much longer Space, namely from 1 to 6 through the Fi g- Io 
Points 2, ?, 4 along the Planes BG, GD. Therefore the Velocity of a Weight is 
always to be meafuid by the Line of its upright A fcent or downright Defcent^ which 
/hews how much it is got nearer to or farther from the Center of the Earth. 

We are to obferve that this Definition relates chiefly to that Part of Mecha- 
nics which con ft den the Anions of Bodies upon one another by the Application 
of Inftruments. 

9. — A Method for finding the Center of Gravity Mechanic ally 
If a Board, of equal thicknefs all over, be laid upon the Edge of a Trian- 
gular Prifm P/>*, or upon the fharp Edge of any ftreight Body placed in an*pj atc 7r 
horizontal Situation, lb as to be in Equilibria-^ whatever Bodies are laid Fig. 4. & 5 
upon fuch a Board in fuch manner that they do not alter its Equilibrium^ 
muft have one Plane of Gravity (that is, a Plane in which their Center of 
Gravity is) di redly over the Edge which fupports the Board. Another 
Pofition of the Body, if the Equilibrium be ftill preferv'd, will give ano- 
ther Plane of Gravity, the Seftion of which Plane will give an Axis of Gra- 
vity, or a Line which has the Center of Gravity in it. A third Pofition 
of the Body may be obtain'd fo as to find a third Plane of Gravity, which 
fhall cut the other two at right Angles, or any large Angle, and the Inter- 
feron of the three Planes will give the very Point which is the Center of 
Gravity. It the Body, whole Center of Gravity you would have, be long 
and flexible, fb as not to lye acrols upon the Board above-mention'd , a 
fecond Board muft be laid upon the firft with a Pin in its Center, lb that it may 
turn quite round without altering the Equilibrium and then long Bodies laid 
upon this laft Board may eafily be mov'd on the Board lb as to find their different 
Planes of Gravity. Thus one may find the Center of Gravity of an humane Body, Plate 7. 
or of any Animal In relation to the humane Body, it is obfervable, that whe- Fi g- 4» & 5-' 
ther a Man be fat or lean (nay in a Skeleton) the Center of Gravity is al- 
ways near the fame Place, viz. in the Pelvis , between the Hips, the 
O/fa Pubis, and the lower part of the Back-bone. Railing up the Arms 
and Legs will raife up the Center of Gravity a little*, but ftill it is always 
fo plac'd that the Limbs move freely round it, the Center of Gravity at 
the fame time moving much lefs than if it was in any other Part of the 
Body. A Statue, though it reprefents a Man, has not its Center of Gra- 
vity in the fame Place as a Man} for if it be hollow, the Hollows are not 
in the fame Places as in a Man's Body, and the Center of Gravity in a 

folid 



74 



Annotat 

Lea. -ii. 



29.. 

Plate 7, 
ig. & 



38. 



3?- 



Plate 7. 



folid naked Statue is higher than in a Man. I mention this, becaufe in let- 
ting up a Statue, and fixing it (efpecially in a Place expoied to the Wind) 
great regard is to be had to place the Center of Gravity over the Middle of 
the Bafe^ or, if the Attitude of th$ Statue does not permit it, then the 
Statue is to be fecur'd raoft ftrongiy on that Side which is fartheft from 
the Center of Gravity. 

Mathematicians, in order to fettle Rules for finding the Center of Gravi- 
ty of Bodies, firfl: give Methods for finding the Center of Gravity of 2 or 
more Lines, then of the Periphery of Figures, then of Planes; for tho' Lines 
and Surfaces do not exift feparate from Bodies, yet they confider Lines as 
ilender homogeneous Bodies, and Planes as extremely thin Solids ; and, from 
that Confideration, more regularly proceed to find the Center of Gravity of 
Solids. Dr. Wallh \m fully treated of this Subjeft in his Mechanics, in 
his Chapter de Inveftigatione Centri Gravitatis, and Monf. Ozanam in the 
third Chapter of his Statics, in the fourth Volume of his Courfe of Ma- 
thematics. 

I lhall give here fome of the moft eafy and ufeful Methods, and muft 
refer the more curious Readers to the Authors above-rnention'd, and other 
Mathematicians that have particularly confider'd the Center of Gravity. 

If a Line be confider'd as an homogeneous Wire infinitely diminiih'd^ 
its Center of Gravity will be in its Middle Point as the Point I in the 
Line AB # . Let there be another Line as CD # in any Pofition in refpeft 
of AB; then if from the Center of Gravity I of AB, a Line (fuppofed 
without Gravity) be drawn to K the Center of Gravity of CD, you will 
have their common Center of Gravity at G by this Analogy, 

** AB X CD : CD: : KI:IG. 
And if the Second Line had been lefs than A B, as for example, if FI? 
had been taken inftead of CD, the common Center of Gravity would 
have been at becaufe **AB.xFE : FE : : K.I : I R 

If there be three Lines (whether they include a Space, fb as to make 
the Periphery of a Triangle, or not) their common Center of Gravity may 
be found after the fame manner as that of three Bodies *. So like wife 
may be found that of 4 or more Lines, and confequently of Polygons. 

It is to be obferv'd that the Center of Gravity of plane Surfaces is not 
the fame as the Center of Gravity of their Peripheries, unlefs when they 
are regular. Thus in the Triangle * AJB C, which is not equilateral, the 
"Center of Gravity of the Periphery will be found at H, nearer to the An* 
gle B than I which is the Center of Gravity of the Triangle. For 
(by 39) D and E being the Centers of Gravity of the two Lines AB and 
BC, F is found to be their common Center ef Gravity, and H the com- 
mon Center of Gravity of the three Lines AB, BC, and CA. 

To find the Center of Gravity of a Triangle, draw a Line from the 
Middle of any Side of its oppofite Angle as G B: Let G I be taken r.| 
of the find Line , and the Point I will be the Center of Gravity of the 
Triangle. Now as every rectilineal Figure may be divided into Triangles, 
the common Center of all the Triangles ill be the Center of Gravity of 
the Figure* Let 





*fe of Experimental Phi 



■Let-* AB and CD be two Quantities (whether Surfaces or Solids) Annotat. 
whofe particular Centers of Gravity are at F and G, the Center of Gra-Lecl. IL 
vity of their Sum, or of A D, will be at * E j but if you would have the v^-v~n. 
Center of Gravity, of the Difference of two Quantities, their particular Cen- * pla ^ e 
ters of Gravity being known j (as for Example, the Center of Gravity of *f 
CD which is the Difference of the two Quantities A B and AD, whole 
particular Centers of Gravity are F and E ft draw FE and produce that 
Line towards G, and you will find the Point G the Center of Gravity re- 
quired, by this Analogy CD : AB :: FE : EG. That is, As the Diffe- 
rence is to the leafl Quantity - y fo is the Line F E : to the Line E G, or the 
Length of the Production of the Line F E. 

The Center of Gravity of a Cone is in its Axis, at the diftance of one * pl 
fourth Part from the Bafej as for Example, in the Cone ABC*, whofe Fi L J 5 K 
A xis is D C, the Center of Gravity will be at F, F D being equal to 

— 4 But in a Conic Surface the Center of Gravity will be diftant from the 

DC 

Bale } of the Axis-, that is, D F will be equal to — . ' 

If A B I K be a truncated Cone, to find its Center of Gravity, let the 
Cone be compleated, which will then be A C B > then having found the 
Center of Gravity of the Cone ABC (namely, the Point F) and the 
Center of Gravity of the Cone ICK (which is the Point E) joyn thofe 
Centers together by the Line F E then confidering that A B K I is the 
Difference of the two Quantities ACB and ICK, you will find its Cen- 
ter of Gravity by the Rule above-mention'd , which will be at G; for 
ABIK : IKC:: EF : FG. 

If a Bucket be made of Copper, Tin, or Wood, in the Shape of a trun- 
cated Cone, the Center of Gravity of fuch a Veflel will not be in the fame 
Place when it is empty as when the faid Veflel is full 5 which Confidera- 
tion is ufeful in feveral Cafes of Mechanics in general, and Hydraulics in 
particular. For by that means Veflels made of the Shape above-mention- 
ed, which being iufpended and moveable upon Pins or an Axis (pafling 
between the Center of Gravity of the empty and the Center of Gravity of 
the full Veflel) fhall turn with the Bottom upwards when empty, will be 
drawn dire&ly up with the Bottom ddwnwards when full ; or on the contrary 
have their Mouth upwards when empty, and turn over and empty them- 
felves as fbon as they are quite full. 

Let ABE D be the Seftion of a truncated hollow Conic Veflel, whofe* Plate 7. 
Mouth is A D. Its Center of Gravity by the Rules above-mention'd will Fi S- 100 
be found to be at c\ but becaufe the Bottom or Bottom-plate BE is of 
fome Weight, the Center of Gravity will be brought down to C. The 
Center of Gravity of the full Veflel (which will be a folid truncated C6ne) 
will be at K. If therefore the Axis of Sufpenfion be placed between thofe 
two Centers, as at O ZFig. 11.3 fuch a Veflel when empty may be drawn* Plate 7, 
up and down hanging with the Mouth downwards, but come up when filling. 
with the Mouth upwards. This is of Ufe in a Chain of Buckets going 

L z round 



j6 



Annotat. 
Left. II. 



Plate 7. 
Fig. 11, 

Plate 7. 
Fig. 1 3- 



PI 7. 
Fig, 14. 



Plate 7. 
Fig- 15- 



ACourJe of Experimental Philofophy. 

round an Axis or Rag-wheel to draw Water from a Depth and deliver it 
in a Trough above. 

But if abed be fucli a VefTel, only with this Difference, that the Bot- 
tom is fixd to the narrow Part ed, and the Mouth is at ah. The Center 
of Gravity of the empty Velfel (without confidering the Bottom) is at c 7 
but by the Weight of the Bottom brought to C. The Center of Gravity 
of the full VdTel will be at K. If fnch a Veffel be fulpended between 
thofe Centers, as at O {Fig. 13.) it will continue with the Mouth upwards 
when empty } but turn over as foon as it is full. Such a Bucket may be of 
Ufe to raife Water by a Machine made with a couple of Buckets fix'd to a Beam 
which moves upon a Center unequally diftant from its Ends, in fuch manner 
that a Bucket fix'd to the Ihorter Brachium raifes up a Bucket at the other 

End, fo as to make it empty its Water in a Ciftern above But a iliort 

Defcription and Figure will make the Thing more plain. 

A A, Are the tw 7 o Spouts running from a Brook or Spring of Water into 
the two Buckets D and E, Dcontaining about 30 Gallons, and being call'd the 
lofing Bucket, and E the gaining Bucket containing lels than a quarter part of 
D^ as for Example, 6 Gallons. 

D E is a Leaver or Beam moveable about the Axis or Center C ^ which 
is fupported by the Pieces F F, between which the Bucket D can defcend 
when the contrary Bucket E is rais'd up. J3C is to CE, as 1 to 4 . 

GL is an upright Piece, through the Top of which the Leaver KI moves 
about the Center L, fometimes refting on the Prop H, and fbmetimes raif- 
ed from it by the Preffure of the Arm CE on the End I. 

The Bucket D, when empty has its Mouth upwards, being fufpended as 
above-mentioned. The End D with its Bucket is alio lighter than the 
End with the Bucket E, when both are empty. By reafon of the diiferent 
Bore of the Spouts, D is fill'd almoft as ibon as E, and immediately pre- 
ponderating finks down to D {Fig. 15.) and thereby raifes the contrary 
End of the Leaver and its Bucket E up to the Ciftern M, where it di£ 
charges its Water, but immediately the Bucket D becoming full pours out 
its Water, and the End of the Leaver E comes down again into its horizontal 
Situation, and ftrikingupon the End I of the loaded Leaver IK raifes the 
Weight K, by which means the Force of its Blow is broke. If the Diftance 
A B, or Fall of the Water be about fix Foot, this Machine will raife the Wa- 
ter into the Ciftern M 24 Foot high. Such a Machine is very fimple, and 
may be made in any Proportion according to the Fall of the Water, theQuan- 
tity allow'd to be wafted, and the Height to which the Water muft be railed. 
" Some Years ago a Gentleman ihew'd me a Model of fuch an En- 
gine, varying fomething from this, but fo contrived as to flop the run- 
a ning of the Water at A, A, when the Leaver D E began to move. 
" According to this he told me that he had fet up an Engine in Ireland 
whiclvraifed about half a Hogfliead of Water in a Minute 40 Foot high, 
and did not coft 40 Shillings a Year to keep in Repair ^ and that it 
was not very expenfive to fet it up at firft. 



ce 

u 
u 



I0 9 [jo,— 



d Courfe of Experimental ThUqfophy. 77 

IOi '[ ?0 .- A Windmill muft be fupported, &c. and a Crane. ~\ This is Annotate 

not ftridly true in Praftice 5 becaufe a Regard is to be had to the Force Left. IL 
with which the Wind pufhes the whole Windmill back with part of its v - ,r V>* 
Preflure, whilft it turns the Sails with the reft.y and therefore the Line of 
region paffing through the Center of Gravity muft fall before the Axis of 
the Poft nearer the Sails. Likewife in a Crape ( I mean fuch a one as whol- 
ly turns round with the Weight) regard is to be had to the Weight which, 
is to be lifted by it \ and the Center of Gravity of the Crane plac'd fo much 
back from the Weight, that the Line of Direftion may only pafs through 
the Middle of the Shaft, when the Weight (which brings the Center of 
Gravity forward) is hanging upon the Crane* 

u, [^2. —the Center of Gravity will remain at reft ? &c] See Sir 

Jfaac Newton's Principia y Coroll. 4th,. of the Laws of Motion,, 2d Editions 
Page 17. 

12. E3 7. — — Demonftrated in the Notes. J Let the Spindle or double Cone 
of * Plate 4. Fig. 14. be reprefented here feen endwife (Plate %. Fig. 1.) AF 
is one of the rifing Rulers upon which the Body is to roll, A G the hori- %> Hv 
xontal Line, B the Vertex of one of the Cones. Let F G the lower part ^ 
of the Screw S be made equal to e E, which is fomewhat lefs than the Se- 
midiameter of the common Bafe of the two Cones } . or ( which is the fame 
thing) let EF be another horizontal Line paffing a little under B the 
Axis of the Cones and BF will be the Way of the Center of Gravity of 
the Body, which Line having a Declivity towards S, the Center of Gra^- 
vity of the Body muft delcend and con fequently bring the Body along, more.; 
or lefs fwiftly, as that Declivity is quicker or flower. 

The Cylinder of Figure 15 Plate 4 is made of light Wood, with a final!* pia te 4- 
Cylinder of Lead at K going quite through it near the. curve Surface and Fig 15. ; 
parallel to the Axis of the great Cylinder, to the Intent that the Center of 
Gravity of the compound Body may be removed from the Axis M into 
the Line RO; and then the Cylinder muft be fo laid on the inclined Plain 
AC, that the Center of Gravity of the faid Cylinder may defcend whilft it 
is rolling towards R, which will make it go up the Plane till the Center of: 
Gravity is fallen as low as it can : Suppofing always a String fix'd to the up : 
per part of the Plane, and, going round the Cylinder to keep it from Aiding, 
when the Plane is not horizontal, as in the Figure.. 

As the Length of the Cylinder does no way relate to its rifing on,, or 
being fupported by, the inclined Plane in confidering the Motion of tfre 
Cylinder onNthe Plane differently pofited, we ihalf in the fecond Figure of 
Plate 8. only confider the Sections of the Cylinder, Plane, and Horiioflvpi ate 
1 PT A is the Seftion of the Wooden Cylinder, C A that of the leaden Fig. 
one, C the Center of Gravity, M the Center of Magnitude, arid- P ^ the 
Seftion of the Plane at firft fuppofed Horizontals 

I fay,, firft, If P a be taken upon PCL equal to 3 PT A, the Jialf Ch> 
cumference or the Cylinder, the Point s will be the fartheft Place to which 
the Cylinder will roll, When . 




\ of JLx^efimentdi Phihfophy 

Annotat, When the Diameter P A going thro' the Center of Gravity C is per- 
L l n ' £?" dicuiar ¥ tl t e horizontal Plane, as in the Figure, the Cylinder will ftand 
w-v-^- ftill, becaule the Center of Gravity is directly over the Center of Mo 
<*No.atf. tion at P * but as Toon as C is ever fo little inclin'd towards Q_, the 
Body will roll till the Point A comes to a defcribing the Semi-Cycloid \ a 
whilft all the Points of the Semicircle apply -themfelves fucceffively to the' 
Line P a, which is the Bafe of the Cycloid. That the Cylinder will go quite 
No. 24. to a, is evident by obferving Cc the way of the Center of Gravity, which is 
not in its loweft Place till it is come to c, and mull afterwards rile to- 
wards k if the Body roll'd on farther- and therefore if by the Velocity 
acquir'd the Body Ihould go on towards Q, the Center of Gravity in go- 
ing down again from k will bring back the Body to a , the Diameter P A 
being again perpendicular to the Horizon, but in the inverted Pofition a p. 
QE. D. 1 

1 fay fecondly, that if the Plane be inclin'd to the Horizon in any An- 
gle whofe right Sine is M C the Diftance of the Center of Magnitude 
from the Center of. Gravity, the Semidiameter of the Cylinder being Ra- 
dius; the Cylinder laid upon fuch a Plane will neither alcend nor defcend 
when the Center of Gravity is directly over the Point T, where the Cy- 
_ linder touches the Plane, provided it be kept from Hiding by a String 

pi ^ !' Sojng under it *, in the manner reprefented in the 1 5 Fig. of Plate 4. 

Fig it • Tu ™ S¥ Cylinder till the Center of Gravity is at K in the fame ho- 
rizontal Line with the Center of Magnitude^ or (which is the fame 
thing) 'till the Semidiameter M A becomes M a ; from K drop the Per- 
pendicular K T, which cuts the Circle at T, and draw the Radius M T 
to which the Plane n 7r being made perpendicular, you will have the An- 
flfJ^P Q- niade b y th e P la ne with the Horizon, equal to the Angle 
M T K, whole Sine is M K equal to M C. For by producing M a to L 
it is evident (by 8. 6. of Euch) that the Angle M T K = K LT, but (by 

In this Situation it is evident by Conftru£Kon, that the Center of Gra- 
*No. 45. vity cannot defcend, becaufe the Line of Direction is fupported at T*, 
where the Plane touches the Cylinder. 

For if the Body was roll'd up any higher on the Plane to bring K to- 
wards 7r, T the touching Point would advance fafter towards it than K does, 
and therefore the Line of Direction would cut the Plane below T towards 
D, lb that the Center of Gravity would defcend and bring back the Cy- 
linder to bear on T. The other way the Body would roll down upon 
moving K ever fo little towards D, the Line of Direction then advancing fafter 
towards D than thePoint of Contact T. This may be made plainer, by confi- 
dering the Cylinder as a Balance ; as for Example, if M iv be a Balance, 
fultaining on its End M a Weight, equal to the Weight of the Cylinder, 
without the Lead, and on the other End w, a Weight equal to the Excels 
of Weight of the Lead, above the Bulk of Wood whofe Room it takes 
up. Let K be their common Center of Gravity, found as has been 
38- taught *: Then confidering KT as an inflexible perpendicular Prop, fuf- 

taining 



taining the Balance at K, the Balance will continue in MquWbro, whilft -\nnotat 

T e £ r0p , 1S ^PPO^^^y bearin g 0" T > the Place where the Plane touches Left II 
the Cylinder. If the Plane, Ihould make a greater Angle with the Horizon, 
the Point 1 being remov'd farther towards L s it would be the lame as if 
the Prop fhould endeavour to fupport the Balance between K and'w in 
which Gafe the Weight M wou'd preponderate, and carry the whole Cy- 
linder towards P h but if the Plane makes a lefs Angle with the Horizon, 
l go towards D, and the Balance then being propp'd between K and 
M the. Weight at w will preponderate and carry the Cylinder towards L. 

C O R O L L A R T. 

Hence follows alfo, that there muft be an Angle iD QJefs than tt D (V 
which will be the Inclination of the Plane, on which the Cylinder above-* 
mention'd can roll to its greateft Height on the Plane. For if the Angle 
7T D Qbe diminifh'da little, the Cylinder will roll towards tt going upwards • 
and if the Plane D Q_be rais'd a little, fo as to make a fmall Angle with 
the Horizon, the Cylinder will rife on that Plane, tho' it will not roll fo 
far upon it as m the horizontal Situation. If this Angle be encreafed the 
Cylinder will rife higher, as its Way on the Plane fhortens, but not be- 
yond a certain number of Degrees of Elevation, at which Elevation the 
Cylinder will go no higher above the Horizon, tho' its Way meafured on 
the Plane will continually fhorten till it is contracted to a Point when 
the Inclination is in the Angle tt D Likewifejts the Angle tt D (V (bv 
lowering the Plane D tt round the Center) diminiftes, the Cylinder wifl ko 
higher as it rolls farther on the Plane, till the Angle is diminilhed to a ■ 
certain number of Degrees, after which the Cylinder will rife lefs: but its 
Way meafured on the Plane will encreafe, till the Plane comes to be hori- 
zontal. Therefore there is an Angle of the Plane iDO, which is a. 
Maximum, as to the Rife of the Cylinder on the Plane. 

I fay, thirdly that the Inclination of the Plane being given on whichpi ate 8 
the Cylinder will rile to the greateft Height (or any other Inclination of a Fig 3 
Plane -on which it can rife at all) the Length which the Cylinder will go on 
the Plane will be equal to the Length TV= T V, which is equal to half 
the Circumference minus the Arc A V, which Arc A V contains twice the 
number of Degrees of the Plane's Inclination, together with the Degrees 
of twice theD.herence of the Angle at the Center of two re&angular". 
Triangles which have MN the Sine of Inclination for Radius, but their . 
Secant* are M R the Semi diameter of the Cylinder,, and MC t he Diftance^ 
of the Center of Gravity from M the Center of the Cylinder. Moreover, 
Tu being the Length of the Cylinder's Progreflion on the Plane, the 
height of the Plane at v, viz. the P&pendicular v Z, will be the Cylinder's 
Kile above the Horizontal Line. 



PREP A*- 




Annotat. 

Left. II. P R E P A R A -ft. I O M 

PQ-is the Horizon and P ^ the Plane of given Inclination. Since P^ 
xuts the Circle PV A, the Cylinder cannot rile upon it, therefore we muft 
take another Plane parallel to it. The Giameter PG being drawn perpen- 
dicular to the Horizon, and RT thro' the: Center of Gravity C or S pa- 
rallel to PG/ draw the Diameter T A, making the Angle PMT equal to 
the; Inclination of, the Plane, and draw 7f perpendicular to that Diameter 
at T, and nV will be a Tangent Plane parallel to the former ^ (for PM T 
being equal to M T R, becaufe of the Parallels PG, R T, and the common 
Angle RT v being taken away, from the two right Angles M T u and 
RTZ, iiTZ the Angle of Inclination of the new Plane n ir, will appear 
equal to the given Angle P M T) draw M R ^ thro' C draw Mf, make 
the Angle X C M equal tp.MCT, produce X C to V and draw M V. Be- 
caufe XCV is one ftreight Line and at the fame Diftance from the Center 
M-as.R.Ty therefore CR and C V are equal (by 7. 3. of Eucl) fince the 
Triangles CM d y C M e are equal (by <5. 7. 8. 1. Eucl) the Angle R.MV is 
biffe&ed. Draw MN the Sine of the Angle of Inclination, and the De- 
grees of the Arc R V, or the two Differences mention'd will be found by 
comparing together the Angle of Inclination and the Triangles RMN 

andCMJST.. . ; V 

The Cylinder being laid on the Plane in the Pofition defcrib'd in the Fi- 
gure, will not only remain at reft, if the Center of Gravity te at S, but will 
return, to that Pofition when moved out of it towards n or towards u, be- 
caufe in each of thofe Cafes the Center of Gravity muft rile, aud therefore 
ST muft be the Diftance of the Center of Gravity from the Plane, mea- 
Hired upon the Line of Direction of the Center of Gravity when neareft to 
the Plane, over that part of the Plane, where the Cylinder rolling upwards 
or downwards will ftop its Motion. Now if the Center of Gravity be 
brought to C, it is evident that C R will be equal to SR, and that C V 
will alfo be equal to it, becaufe by Conftru&ion it is equally diftant from 
Mf a Line going thro' the Center, and confequently mC R j alfo that no 
other Point of the Circumference will be equally diftant from C. Then if 
the Center of Gravity from the Point C in the Line RT, where it is ex- 
aftly over the Point of Contaft, be ever fo little moved towards v by pufhing 
the Cylinder that way, the Cylinder will roll on the Plaiie, and if it ad- 
vances the Length of the Semicircumference till the Diameter T A is in- 
verted and becomes a t, the Center of Gravity will be got to c the Chord 
TR being now t r m 9 but lince r does not touch the Plane, the Center of 
Gravity muft deftend again and bring back the Cylinder till u (which was 
the Point V) returns on the Plane tau, where a K v will be the Chord 
which was mark'd XCV in the firft Eofition of the Cylinder, K being the 
the Center of Gravity and K. u which is equal to C V being in the Situation 
of S T, and the whole Cylinder bearing on v juft as it did on T, when 
we fuppos'd S the Center of Gravity., T A and T R being turn'd into T cc and 



"1 



A Com fe of Experimental Pkilofophy. 81 

Therefore the Diftance T u on the Plane will not be equal to the Aanotat. 
Semicircumference, but want of it the Arc a u = oc u = A V. Confequently Left. II. 
the Length run on the Plane by the Cylinder will be equal to the Arc TV, \*< m \r^ 
which may be found by a Thread applied to the Cylinder from T to V. 

Now the Number of Degrees of this Arc TV may be found in the followingphte 8. 
manner. Fig. 3. 

The Angle of Inclination is v TZ = MTN='M RN = TMP — ■ 
AMG-GMR. ~~ 

^ In the reftangular Triangles M R N and M C N, N M the Sine of Incliiia* 
tionof the Plane is the Radius common to both-, MR the Semidiameter of 
the Cylinder is the Secant in the Triangle M R N, and M C the Diftance of 
the Center of Gravity from the Center of the Cylinder is the Secant in the 
Triangle MCN. The Angle RMN-CMN^RMC; therefore 
R M V = 2 R MC, which may be found by Trigonometrical Tables, and 
confequently it is known. But the Angle of Inclination being given, its 
double is given, therefore AVand TV are known. J£. E. I. 

To apply what has been laid, let us fuppofe the Center of Gravity of the 
Cylinder to be diftant from its Center of Magnitude f of the Radius, that 
is to be at the Point C in the Figure *. * Plate 8; 

The Angle p Ig of the Plane, on which the Cylinder cannot rife is thus Fi S' 
found, by Analogy. 

As MHs toMki: (3:2 ; :) So is the whole Sine : To the Sine of 
the Angle M/i=/MP= plg — 41 0 . 48'~|-,&v. 

The Maximum of the Angle of the Plane on which it will rife mod is 
in this Caie found to be 26% and the Height of that Rife is u Z = 42 85 
fuch Parts of which the Circumference of the Cylinder contains 36b. ' 

N. B. Hence it appears that the Maximum is not in the middle of the 
Angle pig, or at 20 0 . 54', as one might at firft imagine. 

Now let us fuppofe the Angle of Inclination of the Platte to be 15^ 
the Length which the Cylinder will roll on the Plane, and til Height to 
which it will go above the Plane's Bafe will be found not only in the man- 
ner abovemention'd * but alio two other Ways, which for Variety-fake I 
fet down here. 

PREPARATION. 

The Center of Gravity being in the Point C, at f of the Radius of the Cy- 
linder M C from its Center M \ making the ArcfV — Rf, and drawing thro* 
the Center of Gravity C the Line VCX, the Segment VbX is = to the 
Segment R z T, and confequently when the Cylinder has traced on the Plane 
T v the Arc TzV y it will reft and be tequipois'd (on the Plane) upon the Point 
V for the fame Reafon that it is fo upon the Point T before its rolling. 

As the Angle of the Plane v TZ is = 15% that Angle is equal to the 
Angle PMTrr^MR; therefore there only remains the Angle R M V 

M m 



82 A Courfe of Experimental Philofophy 

Annotafc to be found, or its Half RM/j and the two following Ways give the fams 
Left. II. Value for it. 

.VY^ i. Since the Sine G R for the Angle AM R, when the Radius is the 
Radius of the Cylinder, is equal to y C, the Sine of the Angle b Mf for 
the Radius of o C k 9 the Circle of the Center of Gravity: I fay, 

As the Radius of the Center of Gravity : 

To the Radius of the Cylinder :: (or as 2 to 3.) 

So is 00 = 25881^0, the Sine of i5°for the Radius of the Center of 
Gravity : 

To 3882285 = GR or yC, the Sine of the Angle bUf, which is 
found to be 22 0 . 50' A^ .' 

From which therefore fubtrafting the Angle bMR — 15 0 , there will 
remain 7 0 . 50' for the Angle RM/=/M V. Therefore the whole -An- 
gle RMV is ^ i5°. .40'+ s to which adding 30° for the two equal An- 
gles iMR, PMT each of 15°, the whole makes 45 °. 40'+ to be fub~ 
traaedfrom 180, equal to half the Circumference bVzTF of the Cy- 
linder, and there remains the Arc V T for the Length run by the Cylinder 
rolling on the Plane T v. 

2. The other Way to find the Angle RM/ is thus, 

In the Triangle RMC are given R M, MC, and the Angle MRC 
= RM^=i5° 5 therefore I lay, 

As the "Radius of the Center of Gravity : 

To the Radius of the Cylinder : : (or as 2 to 3, or M C : M R : :) 
So is the Sine of the Angle MR C of ' 15°= 2588190 : 

To 3882285 theSineof theAngleRCM, orRC/=:22 0 . 50^ 

And that Angle R Cf being equal to the two oppofite Angles M R C 5 
RMC, or RC /, if from 2 2 °. 5 o' be iiibt railed 1 5 0 for the Angle 'M R C 
= R M b, there remains the Angle fought R M/= y°. 50'+? as before. 

Having therefore fubtraded 45 0 . 40' 4- from 180% there will remain for 
the Arc VZT 134°. 20' for the Way of the Cylinder on the Plain T u, 
that is, 134 j of fuch Parts of which 360 make the Circumference of the 
Cylinder, by which one may find the Height v Z to which it rifes on the 
Plane, thus. 

As the whole Sine: 

To 134! :: 
So is the Sine of the Angle i/TZ. 

To U Z rr 34, 77—. j3i>. E* L 

* Seethe laft 

Edition of 1 3. [39 Common Center of Gravity may be founds &c.*] By this 
Sir ifaac Means may be found the Center of Gravity of our Syftem, in any Pofition 
PrimipiaB 1 lanets Let us firft fuppofe them all on one Side and in a line 

3, Prop. 12. a ? A, going thro' the Sun's Center C: Or to ipeak like an Aftronomer, 

let 



A Courfe of Experimental Philofophy, g g 

let all the fuperiour Planets be in Qppofition, and the inferiour ones in Annotat. 
their inferiour Conjunaion. Firft, the ■common Center of Gravity of Mer-Lcth IL 
cury and the Sun will be very near the Sun's Center* bccaufe the Quantity tvK/~VJ 
of Matter in the Sun is more than a Million of times greater than in Mercury, p ¥ te 8 - 
and Mercury is not 825 Semidiameters of the Sun diftant from the Sun's Flg * * 3 ' 
Center. Secondly, Venus (fuppofing it, as very probable, to have about the 
fame .Quantity, of Matter as the Earth) taken into Confideration, will bring 
the common Center of Gravity of the three Bodies but a little forwarder, 
viz. to 9, becaufe its Mafs is to the Sun's but as about 1 to 169282, and 
its Diftance from the Suns Center but about 145 Semidiameters of the 
Sun. thirdly, The common Center of Gravity of the Earth, and the three 
Bodies abovemention'd, will be brought but to 6, or a little forwarder/ 
Fourthly, The common Center of Gravity of Mars and the other four Bo- 
dies will be brought ftill a little nearer to the Surface of the Sun, as to <?, 
but not half way from the Sun's Center to its Surface. Fifthly, The Quan- 
tity of Matter in Jupiter being to the Quantity of Matter in the Sun, as 
1 to 1067 1 and Jupiter's Diftance from the Sun compar'd to the Sun's 
Semidiameter in a Ratio fomething greater; the common Center of Gra- 
vity of Jupiter and the Sun will be a little way without the Sun's Surface ; 
and therefore the common Center of Gravity of Jupiter and the other 
five Bodies will come to %, a little farther out. Laftly, As the Matter in 
Saturn is to the Matter in the Sun as 1 to 3021, and the Diftance of 
Saturn from the Sun is to the Semidiameter of the Sun in a Ratio fomething 
left; their common Center of Gravity, without the other fix Bodies, would 
be in a Point as h, a little within the Sun's Surface, and therefore the com- 
mon Center of Gravity of all the feven Bodies will be at I, ftiil a little far- 
ther out from the Surface of the Sun, but hardly a whole Diameter diftant 
from the Center of the Sun. When Jupiter and Saturn^ on different Sides 
of the Sun, this common Center of Gravity will always be within the Body 
of the Sun, let the other Planets be in any Pofition," becaufe of their Near- 
nefs, and the fmall Quantity of Matter which they contain. It is this com- 
mon Center of Gravity of our Syftem which is at reft, and not the Center 
of the Sun ; for the Sun has a kind of wabling Motion about this Center. 
The little Difference made hy the Comets and Satellites of the primary Planets 
is not worth mentioning here. 

M- Ltt—Line of Direction falls within their Safe,'] The Tower ofp] a te 8. 
Pi/a is a round Tower 13 8 Foot high, whofe Top over- hangs the Bafe 1 5 Fig. $ and 6, 
Foot, as reprefented in the fifth Figure: And the Tower of Bolonia is 
fquare, 130 Foot high, its Top over-hanging the Bafe only nine Foot. See 
the fixth Figure. 

Animal Motions are always fubjeft to thefe Rule?, which we obferve 
without thinking on them. When we ftand upright with our Feet, as re- 
prelented in Fig. 7. the Line of Direction goes thro' the Point C, and pIat _ g 
palles between our Feet at D, and we may move our Pleads from F to E Fi-. 7, ' 
or G, and our Bodies forwards, backwards, or fide-wife, as far as I or H, * 

M 2 without 



Annotat. 
Left. II 

* Plate 8. 
Fig. icy 



Plate S. 

Fig. 7- 
and 9. 

* Plate S. 
Fig, 9. 

* Plate 8. 
Fig. 8.' 



- Plate 8. 
Fig. 15. 



^ Cowrfe? of Experimental Philofophy. 

without danger of falling or ftirring our Feet, as long as the Line of Di- 
rection traverfes no farther than I A or HB, and fails any where within 
the Space A B which in this Situation of our Feet makes a pretty large 
Baft. But if we fet one Foot before the other, as in Fig. 10 *, a little 
Pnfh fide-wife will make the Line of Direction (which went thro' C) fall 
out of the Bafe to the right or left, towards E or B5 in which Cafe a 
Man muft fall, if he does not quickly remove his Feet to the Pofition of 
Fig. 7 or p. When wefland upon either Leg we muft bring our Body fo much 
over the Foot ABorDE* that the Center of Gravity being diredly over 
it, the Line of Direftion may go thro' ^ orKj and in walking, the Line 
of Direftion muft travel thro' every Place where each Foot is fet down} 
going fucceffively thro 5 the Points E, A, D, B, whilft the Center of Gravity 
goes thro' the Points G,C,F, &c. fo that unlefs a Man, in walking {freight 
forward, fets one Foot direftly before the other, the Line of Direction will 
not defcribe a ftreight Line upon the Plane where the Man walks, but 
an indented Line, that is Angles, to the right and left, whilft the Body of 
the Man goes on in a wadling Motion. This we fee in the walking of 
fat People, and all others that ftraddle in their Gate *. The Line of Di- 
rection 



* It is not ftri&ly true that any Man in 
his common Walk fets one Foot fo exactly 
before the other, as to carry on the Bottom of 
his Line of Direfiion in a ftreight Line, asre- 
prefented in Fig. 10 and 1 1 . Became if a ftreight 
Line be drawn with Chalk, it is difficult to 
walk ftreight along it ; but the plaineft Proof 
is the Obfervation of two upright Sticks, of 
about the Height of a Man, the one painted 
white and the other black, and fet up about 
ten Yards beyond one another, in the fame 
Line that a Man walks towards them ; for in. 
fuch a Cafe, tho s he keep one Eye ihut, the 
laft Stick will appear fometimes on the right 
and fbmetimes on the left of the Firft ; and 
the more fb, the nearer the Man comes to the 
Sticks. Rope-dancers*, indeed, go in a ftreight 
Line ; but it is what they have learn'd by 
Art , and inur'd themfelves to by long 
Pra&ice ; yet they muft even after all have 
Helps to keep their Center of Gravity over 
the Rope, They generally fix their Eyes 
on Ibrne dtftant Point in the fame Plane rs 
the Rope. They have commonly a long 
Pole loaded at the Ends with the Balls of 
Lead B, b y by the Motion of which they 
can alter the Pofition of the common Center 
of Gravity of their Body and the Pole ; as 
for Example, the Center of Gravity of the 
Rope-dancer C A being at A, his Line of 
Direfiion lhouid go thro* a 9 off from the 
Rope ; but by moving the Pole towards B, 



the common Center of Gravity of the Man 
and Pole is brought to C, in which Cafe the 
Line of Direction C D goes thro 9 the Rope. 
Thofe who are well skill'd in this Art will 
fometimes ufe their Arms only, inftead of a 
Pole ; and it is very common for feveral of 
them to dance with a Flag, with which they 
ftrike the Air the fame way that the Center 
of Gravity goes when the Line of Direftion 
does not go thro' the Rope ; and, by the 
Rea&ion of the Air, the Center of Gravity is 
brought back to its proper Place. 

T/jqfe that would enquire farther into this 
Matter^ may confult J. A. Borelli, in -his Book 
De Motu Animaiium, Chap. 18, ip, 20 and 
21. In the Jaid ziji Chapter he gives an Ac- 
count of the Motion of an Horfe, part of which 
(as it is very curious) I flo all repeat here. 

The Ancients obferving that Horfes and 
other Quadrupeds, in Galloping, lift up 
their two fore Feet, and then their hind 
Feet, as fbon as the fore Feet are fet down> 
did imagine, that in Walkings as well as Pa- 
cing and Trotting ', an Horfe has |wo Feet off 
of the Ground at one time ; and accordingly 
in their Brals or Marble Statues, they have 
reprefented their Hoiies with tw^> Legs oif of 
the Ground diagonally oppofite, as the right 
before and left behind, or left before and 
right behind. The modern Statuaries have 
alio fall'n into the fame Error., becaufe in the 
quick walking of an Horfe the Eye cannot well 

diftinguifh^ 



A Courfe of Experimental Philofophy. 8 5 

^eO:ion going thro' the Points AjBjC^D, E, defcribes a ftrcight Line inAnnotat. 
Fig. 11,. where the Feet are let before one another but when the Motion Left, IL 
of one Foot is in a parallel Line with the Motion of the other, an in- -^v-n^ 
dented Line is defcrib'd by the Center of Gravity above, and the Line ^. ate s < 
of Direction as it cuts the Ground at A* B, G, D, E, Fig. 12. Ducks, ^ I0 > 11 
Cede, and the greateft part of the Water-fowl, whofe Legs are let wide l2 * 
aiunder for the Conveniency of their fwimming, and turning quick in the 
Water, have always a wadling Motion uppn Land; but a Cock, a Stork, 
an Oftridge, and moft other Birds that are not web- footed, walk almoft 
dire&ly forward, without wadling (efpecially when they walk flow) having 
their Legs fo plac'd as to put one Foot before the other with greater Eafe. 
Thus Quadrupeds leldom or never waddle,, becaufe they have commonly 
three Feet upon the Ground at a time : So that however the Bale receiving 
the Line of Dire S ion alters from a quadrangular to a triangular Figure ^ 
that Part of it, in which the Line of Direction Tails, : is always in, or 
near the lame Line. 

When a Man ftands in a firm Poftiire # , A B, the Diftance of his Feet, * p larc 
is the length of a quadrilateral Figinre, whole Breadth is nearly the Length Fig, 7. 
of the Feet, and D is the Point under the Center of Gravity C, where the. 
Line of Dire&ion falls. Let the Lines AC and BC be drawn, then let 
thofe two Lines and DC be continued to the Pojnts EFG, lb as to make 
the Triangles ECG and AG B equal and fimilat As long as the Line - 
E D (or a Plane going thro' it) cuts the whole Bod^ of the- Man into two 
equal Parts, the Center of Gravity will be at C, and CD will . be the 
Line of Direction. But if the Body be inclin'd towards the left Hand H, 
the Center of Gravity will move from-C to H, the Line .of Direftion will 
become H B, and the right Foot being eafily remov'd from A may be car- 
ried on beyond B, by which Means the Man will go on towards the left 1 



diftinguim, and therefore he has fhewn from 
Mechanical Principles, that the Motion of 
raifmg two Feet at once in Walking can- 
not be confiftent with the Wifdom and Sim- 
plicity of Nature. To Borelli therefore I re- 
fer the Reader, who wou'd know what the 
Motion is nor, and only copy from him, 
here, what the Motion is. 

* Plate 8. ' ^et us confider an Horfe * 
Fig* 14* * as an oblong Machine fuftain'd 

* by the four Legs, as four Props 

* or Columns, reftingon the Points A B C D; 

* which make a rectangular quadrilateral Fi- 

' gure; then the- Line ef Difeftiofl^will fall 



quently carries on the Line of Direftion 
from E to G, as it felf moves from C is to F;' 
this done, immediately the Foot B is rai$*d,- f 
and carried forward as far as H, which Mo- 
tion of the Foot is eafy , becaufe the Line of 
Direction firft falls within the Triangle A B 
D, fecondly within the Trapezium A B F D; 
that is, the Body of the Horfe is fuftain*d by- 
three or by four Columns. Laftly, the three 
Feet A, D, F remaining firm, and taking in 
the Line of Direction at G, immediately the 
left fore Foot B is carried forward to H; 
and, by the Impulfe already made^ the Cen- 
ter of Gravity is alfo carried over I, namely 



* perpendicularly on E, a Point in or ne^r the • the central Point of the. Rhomb AHFD: 

* Center of the quadrilateral Figure, tfhich * The Motion of the two left Feet being com- 

* will make the Station or Standing of tn e * pleated, the Impulfe and Motion of the; 
' Horft the moft firm. The progreflive Mo- * right hind Foot D begins* and then that of 

* tion begins by one of the hind Feet, for * the right fore Foot ; and fo on in the Man- - 

* Example, the left hind Foot C, which by * ner above defcribcl, as the Animal moves 

* ftrongiy prefTmg back the Ground movtfs for- * forward. 

* ward the Center of Gravity, and confe- . la* 



A Courfe of Experimental TU 

Annotat. In like Manner by inclining towards I the Line of Dfre&ion will be re- 

Left. II. moved to I A, and the Man go to the right. When a Man ftands upon 
o*VXJ one Foot, it is with fome Difficulty. For Example, let the Line of Di- 

Pkte^8. region be CD^ by the Motion of the Blood, and Lungs, and other Ani- 
- mal Motions, the Center of Gravity will be apt to vacillate or totter to- 
wards F or G on either Side about the Center of Motion D, where now 
the Bafe is but fmall. If the Line of Direction comes to B the Man muft 
fall forwards, backwards if to and tho* A be under the Heel of the 
Foot, yet in the Motion of the faid Line of Diredion from D to A the 
Body will be apt to go too far towards E, and fo bring the Line of Di- 
reftion beyond the Bafe. This will more probably happen in the fide Mo- 
tion of the Body 5 fo that the Body will be in danger of falling, unlefs 
the right Foot be put down towards that Side where the Body inclines. 
Birds Hand upon one Foot much more eafily than Men, becauie their 
Line of Direction being much fliorter, and the Bale of one Foot a large 
Rhomboidical Figure made by the four Claws, the Line of Direction cannot 
go out of that Bafe, unlefs the Center of Gravity riles, which is impof 

* 28, 43. fible without a violent Motion * 

When a Porter carries a Burthen upon his Shoulders, he miift ftoop, 
becaufe if he fhould ftand upright, the common Center of Gravity of the 
Man and Burthen would be fo far brought back that the Line of Direc« 
tion would fall behind the Feet. For the lame Reafon, when a Woman 
with Child is very near her Time, ihe bends backwards as ihe goes, by 
Reafon of the Burthen before, which otherwile would caufe her to' fall 
forwards. 

gate 9. IJ# [ 49 . Roll along the Planed If the Ball * FE be laid upon a 

"** *' fmooth horizontal Plane AB, it will ftand ftill, tho 5 it touches but in one 
Point as O, becaufe the Line of Direction' C O goes thro* the faid Point j 
but if the Plane be ever fo little inclined to the Horizon, as in the Pofi- 
tion C D, the Ball will continually roll forward towards D, becaufe then 
the Line of Direction will always fall before the touching Point. 
Plate 9. If fuch a folid Body as G, contain d under twelve reftangular Parallelograms 
J?ig. a and 3. anc j two 0 pp 0 fite, parallel and equal Dodecagons, be laid upon the inclin'd Plane 
B AC, as it will Aide from A to C, the Center of Gravity moving in the 
Line eg parallel to the Plane DC, and io one of the parallelogram Planes 
of the Body always touching the faid Plane A C. But if the Plane be 
more inclin'd, as in the Pofition BE, it will appear, by drawing the Arc 
e f with the Diftance ie about the Point * (the only touching Place of the 
Body then) that the Center of Gravity can delcend } and when the Point 0 
is applied to the Plane DC, the Line of Direction will fall beyond the 
faid Point 0 towards and therefore the Body will roll or tumble to- 
wards E. In the lame Manner all the angular Points, or rather the Edges 
of the Plane Surfaces, will fuccefilvely apply themfelves to the Plane D E 
till the Body has roll'd quite down. 

16. [49— 



A Courfe of Experimental Phihfophy. 87 

16, C49 In the Load of Iron the Center of Gravity is low 0 hut wry Annotat.' 

high in the Load of Hay. Left. II. 

K * is the common Center of Gravity of the Load of Hay and the Car- V «^V S ^ 
riagePM, whofe Line . of Direction isKE, whilft the Plane PM-(on|J ale 
which the Carriage is drawn) is horizontal } but if C D be an horizontal Line, s * *' 
the Plane P M will be inclined to the Horizon in the Angle B P D, and the 
Line of Direftion being changed from KE to K P (becaufe K P is the only 
Perpendicular from K to CP> will fallout of the Bale QJV1 towards C, and 
confequently the Waggon will be thrown over that way } which alfo appears by 
drawing round the touching Point CLwith the Diftance Q_K, the ArcKR 
ihewing the Way of the Center of Gravity, which can in this Cafe defcend 
without firft riling, For the fame Reafcn, if the Carriage was drawn along 
an Horizontal Plane, whofe Se&ion is reprefented by CD or P N ? and the 
Wheel M ihould meet with a Rub of the Height of N M, the Load of 
Hay would alfo be overthrown upon that Account. 

But as a Load of Iron * lies much lower upon its Carriage, the Cen- Plate 9. 
ter of Gravity muft alio be lower, and therefore the Line of Dire&ion Kg- 5* 
will fall within the Bale- on the fame Inclination of the fupporting Plane, 
as would occafion it to. fall out of the Bale in a Load of Hay, as is evi- 
dent from the Figure. Let C D alfo here reprefent an Horizontal Line, 
and QJVf the Road or the Bale fupporting the Carriage, the Angle of In- 
clination M CLN in this Figure being equal to M Q_N in Fig. 4. The Line 
of Direction K P will here fall within the Bafe QJV4, and cannot fall out 
of it till the Angle of Inclination is encreas'd to BQJf, by making XI 
the Horizontal Line} or, which is the lame Thing, unlefi the Wheel M 
meets with a Rub of the Height of yM much higher than the Rub which 
would overturn the Load of Hay* 



88 



LECTURE III. 

Left. III.*- Qflmple Machines or Organs J call'd by fome Mechanical 
s-^V-v. k3 Faculties, or Mechanical Towers % are fuch Inftruments 
Anuot. i. as are 0 f one pi ece (q V confider'd as fuch) by means of 

*L.2, ip, which the * Towers defcrib'd in the laft Leclure a£t upon 
2# - Weights, in order to give or ftop Motion ; to overcome, make 
or flop Refiftance. 

2. All Engines (however compounded) for the Ufes of Life, 
are made up of various Combinations of the fimple Machines. 
Sometimes all of them may be found in one Engine ; fome- 
times two or three of them; and fometimes only one of the 
Mechanical Powers multiplied,, 

9. The Simple Machines are the feven following, viz. the 
Balance, the Leaver \ the Tulley, the Axis in Teritrochio (or 
Axle in the Wheel) the Inclined Tlane, the Wedge, and the 
Screw. N. B. Authors differ in their Enumeration of the Me- 
chanical Powers, fome making them to be Six, excluding the In- 
clined Plane from thofe which I have nam'd. Others have re- 
duced them to Five, confidering that the Screw is only a Wedge 
carried round a Cylinder : And others again have made the hea- 
ver and Balance to be the fame Power, from their near Refem- 
blance* But fince the fame ^Principle is only applied different- 
ly (as may be fhewn by reducing all the Mechanical Powers to 
/^ Leaver, or explaining all their Operations by that of the Lea- 
^Annot.a. ver*) and we are to give an Account of the Infiruments con- 
trived for that different Application^ the Mechanical Powers will 
appear to be Seven. 

4. Before we explain thefe Powers or Organs feverally, there 
are fome general Things to be confider'd relating to all En- 
gines, which will facilitate our Calculations concerning them, 
and render the Execution of them in Pra£tice, as perfe£fc as the 
Nature of the Materials of which they are made will allow. 

SVT- 



A Courfe of Experimental PMIoJbphy, 



89 



S V T T 0 S I T I 0 N S. 

5 . Tho' the Earth be fpherical, yet we are to fuppofe it Left. Ill 
flat, when we confider Mechanical Engines ; becaufe the largeft l - r VV 
Machine covers fo fmall a Part of the Earth's Surface, that to 
allow it any fenfible Roundnefs in fo fmall a Compafs, would 
fee to allow too much. 

o none of the Bodies which we handle are perfectly 
hard, or truly of the Figure which we intend to give them; 
yet we are to fuppofe every Thing perfeft in all our Engines ; 
as for Example, that ftreight Bodies, as the Beam of a Bala?tce, 
a Leaver^ Sfc. are Mathematical Rigids^ and wi:hout Thicknefs, 
or Lines altogether inflexible ; that the Mechanical Towers 
(whether Simple or in Compofition in complex Engines) are 
without Weight, whatever Materials they are made c6f ; that 
Bodies are perfe£tly hard and fmooth; that the Parts of En- 
gines move one another without Fri&ion; that Cords are ex- 
tremdy pliable ; that the Center Pins of Pullies, or Axes of 
Motion of them, of Balances, Leavers, Axes in Teritrochio^ &c. 
are only Mathematical Lines. 

7. Tho' the * Lines of Dire&ion of all heavy Bodies tend * l. 2. 22. 
towards the Center of the Earth, and confequently converge 
together in a fmall Angle* yet we muft confider them as pa- 
rallel, becaufe they are fo, as to Senfe; their Point of Conver- 
gence being near 4000 Miles off For this Reafon the Walls 
of a Building, when exactly adapted to the Plumb Rule, are 
nearer at Bottom, than at Top; tho 7 in Practice we muft al- 
ways look upon them as parallel. 

6 Notwithstanding the Falfity of the Suppofitions, we fliall 
not be led into any Error by them ; becaufe, by a fecond Con- 
federation, we are to have regard to the Imperfe&ion of En- 
gines and Materials, and the Quantity *of Stickage or Fri&ion ; 
which differ according to the Number and Combination of 
Parts and Nature of the Materials, of which the feveral 
Engines confift : And having made ufe of the beft Me- 
thods we can to difcover the Imperfections abovemention'd, 
in each particular Machine ; we are to take care to allow 

N enough 



9o A Courje of ^ Experiment aX Phikfopfy, 

Led. III. enough to be deduced from the Calculation made concerning 

l/WJin TJrxTlno K,~ n r.n*X A/T^t __11„ ^ O 



N. B. Several Methods of finding the Quantity of Fviffwn 
Ann. 3. in Engines will be confide * 



and L . 4 



D e f 1 n 1 r 1 0 if s. 



9.. When equal or unequal Quantities of Matter are fo ap- 
plied to a Mechanical Organ, or Engine, that their Momenta^ 
or Quantities of Motion, or moving Forces,, deftroy one ano- 
■ i-'ther ; they are laid to be in Mqmlibrio *. 

10. When Powers, whofe Intenfities are equal or unequal,, 
are fo applied to an Engine as to deftroy each others A&ions* 
* L. a. u; tne y are t0 t> e * n Mquilibrio 

1 iv All Bodies that a€t againft each other by means of En- 
gines, may be confider'd as Towers and Weights, already de« 
fcribed in Le£t. 2^ N°. 18, 19. 

12., Bodies in ^Equilibria are faid to equiponderate. 

13. When Powers antf Weights have their Velocities red- 
*L. 2. 10. procally as their Maffes,, or as their Intenfities *, their Moment® 
t> are equal ; therefore they are in Mquilibrio -f%. 

T4.. If. the Momentum of a Power be greater than that of the 
Weight, or (on the contrary) the Momentum of the Weight be 
greater ; that Power, or Weight is faid to preponderate., or o*~ 
ver-poweiv 

^ - 

15. When, either the Velocity (the Mafs being equal) or the 
Mafs or Intenfity of a Weight or Power (the Velocity being e- 
qual) or both Mafs and Velocity, together are greater in a Pow- 
er or Weight than in the oppofite (or counter-a£ting) Weight 
or Power ; the Momentum of the former will be greater than, 
*"L,a. 1-5, that of the latter * 

17, N. B. This will happen, let the Difference be ever Jo /kail; 

tho' then the Rejiflance made by the Friction* will hinder the Ef- 
$B from king vi/ible> 

Of 



Of the BALANCE. 

16. The eflential Parts of a Balance are (1.) the Beam, as Led. Ill 
B *; (2.) theAxis of Motion, confider'd only as a Point or ty-v^o" 

Center of Motion C, which divides the Beam into two Parts •* Plate 9 - 
(3.) thofe Parts call'd the Arms or Brachia, as AC and C b' Fig ' <Jand7 ' 
which are either equal, as mFig. 6, or unequal, as in Fig, y. 
(4.) the Points of Sufpenfipn, as * A, B, in the 6th, and A,** Plate 9. 
B, K, jc, in the 7th Figure. Fig. tf. 

17. When Weights hang Freely from the Points of Sufpen- 
fion, they gravitate neither more nor lefs for hanging nearer 
to or farther from the faid Points. 



Experiment I. Tl. 9. Fig. 6. 

18. Let the Weight Q, with its Rope QA hanging at the 
End A of the Balance A B, be equal to the Weight P, toge- 
ther with its Rope D B. Hang the Weight P at any of the 
Loops G, F, E, D, of its Rope, and it will at any of them make 
an Mquilibrium with the oppofite and equidiftant Weight Q. 

19. When the Beam of the Balance is equally divided by the 
Center of Motion (as in the 6th Figure) with Scales hanging 
freely from the Points A, B, inftead of the Weights Q^and P, 
it. is the Libra j or common Tair of Scales. 

* 

ac. This Inftrument ferves to compare together Bodies which 
have equal Quantities of Matter, tho' fometimes differing in 
Bulk. J for when the Commodities to be bought or fold are 
placed in one Scale, fo as to keep the Weights in the oppofite 
Scale in JEquilibrio J the Momenta are equal ; and fmce the Ve- 
locities are equal on account of the equal Diftances A C and 
C B * the Quantities of Matter muft be like wife equal; and this*r 2 . 
is Ihewn by the horizontal Pofition of the Beam hanging freely 
on its Center of Motion, which is plac'd a little above its Cen- 
ter of Gravity. See the 4th Annotation. Ami. 4.' 

Hence follows, that the Diftance (that is the acting Di- 
ftance) of any Weight is not to be meafured from the Cen- 
ter of Motion of the Balance to the Center of Gravity of the 

N 2 Wciaht; 



92 AQur/e of Experimetrf^P^ 



Left. III. Weight; and therefore the Lines Cn, C m 7 do not exprefs the 
Diftances of the Weights P and Q; but their Diftances are 
properly C B and C A, the leaft Diftance from their Lines of 
Dire&ion N n ^nd Mm to the Center of Motion C : And 
therefore when the Weights hang freely upon an Horizontal 
.Balance," -the Diftance of their Points of Sufpenfion from C may 
be callM their Diftance and meafur'd upon the Beam ; but if 
the Balance be in an inclin'd Pofition as a b r not bC and aC, 
but d C and eC will be the Diftances of the Weights f and f, being 
Lines perpendicular to their Lines of Direction j> 0, q and 
going thro' the Center of Motion, confeq^iiently the leaft Di- 
ftances from it to the faid Lines of Dire£tion* 

*Pl. ^Fig. The Balance, whofe Brachia are unequal *, as A B {Ftp. 

.?•■ 7.) is the Roman Stat era, or our Steel-yard; or the little In- 

urument which the Chine fe (who take all their Money by 
Weight) always carry about 'em, call'd the Dotchins. See Num. 
fg. of -Left. 2, Tlate 4. Fig. 3. This Inftrument ferves to 
compare, together, at one Operation, Bodies that have equal 
or unequal Quantities of Matter, but in weighing heavy Goods, 
it is not fo exact as the Scales. 

*Pi.j>,Fig. ' The * Balance of Fig. 8. may ferve as a Steel-yard or as 
a Pair of Scales, on account of the feveral Divifions on each 
Brachium. 

T H E O R E M. 

22. One or more Weights fuff ended on one 'Brachium of a Ba- 
lance, will be in ^Equilibrio with one or more Weights fufpend- 
ed on the other Brachium ; provided that the Sum of the Mo- 
menta (or the whole Quantity 1 of ' Motion) of the Weights on 
one Side of the Center of Motion^ be equal to the Momenta on 
the other Side of it. 

Experiment II. TL g. Fig.d*, 

23. Upon the Brachium AC hang three fingle Pounds at 
the Divifion 8, a fix Pound Weight at Number 5, a three 
Pound Weight at Number 1, and a nine Pound Weight at Num- 
ber 3/ Then on the Brachium C B, hang a two Pound Weight 



A Courfe of Experimental Philofophy. 93 

at 2, a twelve Pound Weight at 5, and a two Pound Weight atLe£t. III. 
10. Then the Balance will hang in Mquilibrio. 

24. Since the Velocity of Weights hanging to a Balance de- 
pend upon their Diftances from the Center of Motion, each 
Weight being multiplied by its Diftance from that Center will 
give its Momentum: Therefore 8 X 3 (= 24) -h 5 X 6 (= 30) 
-4-3 x 1 (= 3) + 3 X 9 (r= 27) make up the Sum of 84 for 
the Momentum or Quantity of Motion on the Brachium A C : 
And 2X2 (=4) + 5 X 12 (=6o)H- io X 2 (—20) make 
the like Sum 84 for the Momentum on the Brachium C D : And 
eonfequently thefe equal Momenta acting in contrary Directions 
muft produce an ^Equilibrium * If all the Weights on the Bra- * 9. 
chium AC were reduc'd into one, viz. a twenty-one Pound 
Weight hanging at the 4th Divifion, it would keep in Mquilibrio 

a Weight equal to all the Weights on the Brachium C D hang- 
ins at a quarter of a Divifion beyond the 5th, becaufe 4X21 
~ X 16 = 84, as has been fhewn in the fecond Lecture *; * %i -m. 

P R O B L K M: 

25. Equal or unequal Weights being fuff ended at the Ends of 
a Balance of known Length and Weight. How to find the fix d^ 
Toint or Center of Motion about which the faid freights will} 
be in iEquilibrio. 

E x p e r 1 m e n t III. PI. 9 . Fig<7° 

A B is a Balance weighing four Ounces, and of 12 Inches 
in Length, at whofe Ends A arid B are fufpended Weights of four 
and eight Ounces. Find out the common Center of Gravity or 
the faid Weights * which will be difeaiy under the Point 4t 1 
Numb. 4. Let K be made the Center ^ Motion, and the% 
the Center of Gravity being at its loweft Place * the Problem 
will be folv'd, if the Balance A B has no Gravity. But as the 
Balance weighs four Ounces, the Brachium A K will over-weigh 
the Brachium KB, and fo deftroy the ^Equilibrium. Now a 
fecond Operation like the former , will perfeaiy folve the 
Problem, after the following Preparation. Sufpend the Weight 
E equal to the two former Weights or 1 2 Ounces at the Hook 
under K at the common Center of Gravity of the two Weights; 

wlnclx 



L. 2,- 



94 A Courfe of Experimental Phihfophj, 

Left. III. which reducing their Weights into the Center of Gravity, they 
^(py^y w ^ as before * : Reduce alfo the Weight of the Balance in- 
" z * 54,4 to its Center of' Gravity, by hanging the Weight D of four 
Ounces (or equal to the Weight of the Balance) at % under 
6 the Center of Magnitude, which is alfo the Center of Gra- 
vity, becaufe the Balance is regular and homogeneous. Then 
fhall we have the fhort Balance 64 or * K without Weight, 
and the Point C or true Center of Motion will be found by 
this Analogy, E-HD (16 Ounces) : D (4) : (or a Length of 
two Inches ) : KC (or half an Inch.) This Point will be direftly 
over the Center of Gravity of the Balance and all the Weights ; and 
taking away the Weights D and E the \ Mquilibrium will remain, 
the Alteration of the Center of Motion from K to C making a- 
mends for the unequal Weight of the Brachia of the Balance. 

T R O B L E M. 

2 6. A given Weight hanging at one of the Ends of a Balance 
of known Weight, to find the fix' } a f Point about which the Ba- 
lance and Weight will be in iEquiiibrio. 

Experime N t IV. *PL 9. Fig. 9. 

Having fufpended the given Weight D equal to four Pounds 
(for example) at the End A of the Balance A B, which weighs alfo 
four Pounds; fince the Weight of the Balance is confider'd in 
this Operation, we muft fuppofe the whole Weight of the Ba~ 
l/c 4}. lance reduc'd into its Center of Gravity *, as if the Weight E 
of four Pounds hung at C the Center of Gravity of the Balance, 
which is at its middle Divifion 6 : then we fhall have a new Ba- 
lance (vis. A C) without Weight, at whofe Ends hang the Weights 
D and E, whofe fix'd Point will (by the laft Prop.) he found at 
3 ; or more generally by this Analogy. 

As D + E (or the Weight of the Body and the Weight 
of the Balance): 

Is to E (The Weight of the Balance) : : 
So is C A (Half the Length of the Balance) : 

To A 3 (The Diftance of the fix'd Point from the given 
heavy Body.) 

T R 0- 



A Courfe of Experimental PHlofophy. 9 $ 



PROBLEM. 

27. To make a deceitful Balance or Pair of Scales, whofil^Qi.TLl. 
Beam will hang in iEquilibrio without the Scales, or with the ^"V^w 
empty Scales ; and yet Jh all alfo be /V JEquilibrio when unequal 
Weights are placed in the Scales ; fo as to cheat in any Propor- 
tion intended in making the Balance at jfirji. 

This Problem is folv'd by making a St at era or Steel-yard with 
the Appearance of a common Beam, as in the following 

Experiment V. 5P/. 9. Fig. 10. 

To the Beam A B (23 Inches long, whofe Brachium CB, of 
j 1 Inches in Length, keeps in Mquilibrio about the Point C 
the Brachium C A , of 12 Inches in Length, by being made 
fo much thicker , or having fo much more Matter, as may 
make amends for its being fhorter) fufpend the Scales D, E io 
fuch manner that D, which weighs one Part in twelve lefs than 
E, fhall hang at the longeft end of the Beam, and they will 
keep each other in Mquilibrio • Then placing 12 Pound Weight 
at G in the Scale E> it will keep in Mquilibrio no more than 11 
Pounds of F, the Commodity to be fold if placM in the Scale 
D. Becaufe then, F will be to G, in a reciprocal Proportion 
of BC to -AC*. ' ' *>i 3 ^- 

Tho' fuch a Balance may be fo< nicely made as to deceive the 
Eye; the Cheat is immediately difcover'd by changing the 
Weights and the Commodity F from one Scale to another ; for 
then the Owner of the Balance muft either confefs the Fraud < 
or add to tjse Commodity he fells, not only what was wanting,, 
but alfo as much as he intended to cheat him of, and a Fra&ion, 
of that added Weight proportional to the Inequality of the 
Brachia of the Balance. That is, in this Cafe, the Buyer inftead' 
of ii Pounds offerM him for 1 2 his Due, will have (by chang- 
ing the Scales) 13— Pounds* For whereas in the firft Pofition^ 
of the Balance F (11) X AC (12) was equal to G (12) X BC 
(ir ,) when G or 12 Pounds is plac'd in the Scale D, then 12 
X 1 z will he. equal to no* left than C B. (j 1) X 1 3 -x G ; or, 

As^ 



A Courfe of Experimental Philofophy. 

As the Brachium CB, 1 1 Inches long : 

Is to the Brachium C A 12 Inches long : : 
So will be F, or the Weight 12, plac'd in the Scale D : 
To G— i3 T v r ov the Weight of the Commodity keep- 
ing the Weights in /Equiiibrio. 

And therefore as this Analogy gives a reciprocal Proportion 
between the Weights and their Velocities, the Momenta will be 
equal, which with contrary Directions deftroy one another. 

N. B. In all thefe Cafes wefuppofe the Weight to hang freely 
from thofe Ends of the Balance to which they arefaften*d» See t he 
*Ann. 5. other Cafes in the Notes 

Of the L E AVER. 

28. The Leaver (a known Inftrument commonly callM a Hand- 
fpike, when of Wood, and a Crow, when of Iron) is, in Theo- 
ry, to be look'd upon as an inflexible Line like the Beam of a 
Balance, and fubjeft to the fame Proportions, only that the Power 
applied to it is commonly an animate Power ; and from the dif- 
ferent ways of applying it, it is calPd a Leaver of the fir ft ^ of 
the fecond, or of the third Kind. 

Experiment VI. Tl. 9. Fig. 11. 

29. Let the Steel-yard P W be taken off of its Hook K, and 
let its Center of Gravity C be plac'd upon a Fulcrum or tri- 
angular Prifm D E ; and inftead of the Weight 1 hanging at P to 
keep in Mquilibrio the Weight W of 4 Pounds, let an animate 
Power, as the Hand ? be applied at P: The Stat era ox Steel-yard 
will then be turned into a Leaver of the fir ft Kind, Co calPd be- 
cause the Fulcrum or fix'd Point is between the Ends as at Q in 
which Cafe the Power may be four times lefs in Intenfity than 
the Weight; but equal to it, if C or the Fulcrum was removed to 
M (the middle Point of P W) and four times greater, if C was 
removM to 3. N. B. In all thefe Cafes j the Leaver is ftill faid 
to be of the firft Kind 

30. When the Fulcrum is at one End, the Power at the o- 
ther, and the Weight between them, the Leaver is of the 

Jfiatep. mndKind** J 

rig., 1 a.-' 

31. But 



Left. II L 



A Courfe of Experimental ' Philo/bphy, 



tj V' P UT ,it.iSQf the third Kind, when the fix'd Point is at oneLeft. III. 
una, ■ the Weight at the other, and the Rower between them * . 

N.B. The "Power and Weight, are always Juppo/ed to dOr at* ;piate 
right Angles with the Leaver, except it be otherwife exprefs'd; g ' I? " 
fir then the Cafes will vary, as may be feen in the Notes * upon* Ann 5 . 
the Balance, which are equally applicable to the Leaver. 

The Proportions, which the Powers and Weights bear recipro- 
cally to their Diftances, are fet down at the nth, 12th and 
13th Figures. 



Experiment VII. 9. Fig. 14. 

32. Place the three Leavers A, B, D, in fuch manner up- 
on the Fulcra V, F, F, that A may have the Proportion of its 
Brachia as 5 to 1, B as 4 to 1, and D as 6 to 1 ; and let thefe 
Leavers ad upon each other; then making ufe of a Power e- 
qual to one Pound at the End M of the Leaver D, it will 
keep in JEquilibrio W, or 120 Pounds at the End 1 of the Lea- 
■ ver A. 

In this compound Leaver, the 'Proportion or Ratio of the 
Weight W to the Power M is compounded of the feverai Ra- 
tios of the long Brachium of each Leaver to its fliort one; for 
5 X 4 x <5~ i20. And accordingly you will find by meafuring 
the Afcent and Defcent of the Ends of the firft and laft Leaver, 
that whilft the Weight W defcends h of an Inch, the Power or 
little Weight M will afcend VV or 12 Inches, the Force to be 
gain'd by fuch a compound Leaver being fhewn by the re- 
ciprocal Proportion between the Manes and Velocities of W and 
and M. 

When two Powers applied to the Ends of a Leaver, fup- 
port a Weight refting upon the Leaver, they are to one 
another reciprocally as their Drftances from the Weight* The 
Proportion is mark'd in the Figure \ * Plate 9 

Fig. 15." 

E XPERI M E N T VIII. Tl. 9. Fig. 16, 

35. In the Frame A B C D hang the Leaver E F at the Points 
I, K, loaded with the Weight 7 at C ; and the Weights whofe 
Ropes go over the Pullies G H, being to one another recipro- 
cally as the Diftances I C, and C K, will keep in Mquilibrio the 

O feven 



another as 3 #04 Center of Gravity for IPomt C) 
mtfi be Verrim'd a liPt k ' farther towards 1, m was pud before 
cbMerWftg the Balance 

It is upon this Principle that Horles of unequal Strengt 
may draw equally in a Coach ; for if the Spring-tree Bar be une- 
qually divided, that Elorle muft employ more Strength which 
is applied to the ftiort End of the laid Bar. Two Men alio 
who carry a Barrel hanging from a Staff are unequally prefs'd 
upon their Shoulders, if the Barrel does not hang in the mid- 
dle, the Man carrying moft who is the neareft. This is farther 
illuftrated by 

EtPERittEN T IX. '5V.'4» Fig. 17. 



34. The Foot F fupports an horizontal Board A B, on which 
ftvuft be laid the Leaver 1 2 divided in the Proportion of 2 
to 1 (fuppofing it a Spring-tree Bar) then placing the Pulley it 
over-againft 2, and the Pulley m over-againft 1, let the Weights 
G <i t>) and M (2 f>) hang by Strings over the laid Pullies, 
and if they will keep'in MquilibrioMe Weight N =r 3 ft> draw- 
ing the Leaver in a contrary Direction over the Pulley 0 againft 
C. N. B. The Tnllies Jlide in a Groove in the Edge of the 
MoWd* and Remain in amy, "Place where they are fet. 



Exp erim en t X. Tlate 9. Fig. 1-8. 

If there be =a Leaver whofe Bmchia make an Angfe } 
as is reprefented in the Figure, with its fix'd Point at the An- 
•gfe as C ; the Weight W, freffing M perpendicularly upon the 
End W, will be fcept ^Mquilibrm by a Weight of one?Pound 
•drawing the other End ^of thrXeaver P -perpendicularly^ (by 
means of a Pulley over which the: Line of Direton of the 
Power is carried) by two Pounds at / and three Pounds at w. 
It is in this manner that a Hammer is made ufe of to draw 
a Nail. Some call this a Leaver of the fourth Kind •, but it is 
evidently a Leaver of the ; firft Kind, becaule the Weight W is 
at one Eni, the Power ;P at the other, and the Center of Mo- 
tion C between: And if the Arm C W be let ftreight nv a 
Li ne «h & m to bring f to ^ and c bz made the 

Fulcrum 




Fulcrum j the Inftrument will plainly appear to be a Leaver Led. Ill, 
*xf the IrftKind *V**~V 

Of the T V L L % T. 

36. When a little Wheel, commonly a Sheave or Sheever h io 
fixM in a Box or Block as to be moveable round a Center-Pin 
p#ng thro' it, fuch an Inftrument is callM a Pulley * : And fome- * , PIate I0 * 
times, thoVimproperly, a Box or Block with ie vera! Sheevers in Flg * u 
it is alfo call'd a Pulley, as in the fecond Figure The fir ft* PL icv 
$>f thefe Is by Workmen a Snatch-block. Fig. z, 

A Rope going round one or more Pullies to raife a Weight/ 
is callM the Running-rope. 

When, a Block with its Sheevers is fb fe'd, that whilft it 
remains immoveable, another Block and Sheevers riles with the 
Weight hanging at it ; fuch a Machine is calfd a Fair of Blocks. 

An upper or fixM Pulley adds no Force to the Power 5 
tout only prevents the Friction by making the Rope run eaiily ; 
md 3b much the more as the Sheever is bigger than the Center- 
fin about which it turns *Ann,8. 



Expe rime nt XI. VL iq. Fig. g. 

Having faftenM to the Ends of a pliable Rope the Weights i 
and 3, the firft of one, and the other of three Pounds, if the 
Rope be thrown over the Square but ftnooth Beam A B, the 
Ifri&ion of the Rope on the /Beam will be ib great as to hin- 
ider the three Pound Weight from railing the one Pound, tho ? 
its Momentum (without that Hindrance) is three times greater, 
becaufe its Velocity is the lame and its Matter triple But* L. %, 3 
if only one Pound be faften'd at the End of the faid Rope, and the 
?R^pe thrown over the Pulley E D, the fingle Pounds will keep 
each other fo exafitly in Mquiltbrio that the leaft Weight added 
to either of them will make it over-power. That thefe Weights 
nought to be in JEquilibriOj appears from a fight of the Figure*, 
fince the Weight on the right Hand cannot defcend to d with- 
out caufing the Weight on the left to afcend up to E precife- 
ly with the lame Velocity, 1 d being equal to 1^. aN* B. -$This 
Wulley is alfo calPd a Roller. 

O 2 qB* A 



IOO 



A Courfe of-Expwim 



Left. III. 38. A lower Pulley, that is fuch a one as is moveable with 
^OTV the Weight, takes off half the Weight; fo that a Power of half 
its Intenfity will fuftain it. 

Experiment XII. Tl. jo. Fig. 4, 

To an Hook coming from the Center of the Pulley £ e hang 
a Weight of 2 lb ; then having made fa ft the running Rope to 
the Hook / of the Arm A, bring it under the faid Pulley g e 
and over the Pulley dj and 1 ib at the End of the Rope will 
fuftain the 2 ib hanging from c the Center of the Pul- 
ley g e. 

That the Power pulling down at 1 ads in the fame man* 
ner as if it pull'd upwards at d is evident, becaufe we have 

* 37- already fliewn that an upper Pulley neither encreafes nor 

diminifhes the A£tion of the Power. 

We may at one View fee in Pullies how the Force of a Weight 
is diminiJOh'd , by confidering how many Ropes ( or Parts 
of the Rope) are employed to raife it, and which divide the 
Weight as they are applied to the lower Pullies to which the 
Weight hangs, ^ whilft the Power only draws by one Rope- 
For Example, in this Cafe the Ropes fe and dg fuftain the 
Weight; but fe is fupported by the Hook f whilft the Pow- 
er only draws up the Rope d g. 

39- From this we may deduce this general Rule to know 
the Advantage to be gain'd by a Pair of Blocks , let their 
Number of Pullies or Sheevers be what it will, (viz.) As 
One is to the Number of the Ropes (or of the Tarts of the Ropey 
applied to * the lower : *Pullies\ fo is the ^ower to the Weight. 

* Plate ia Thus it is evident, only by a fight of the Figures that one 
F%^4> h $ Pound will fuftain 4'ib as in Fig. 5, Six Pounds as in Fig. 6. 
" Five Pounds, as in Fig. 7 : And fix Pounds as in Fig. 8. 

N, B. The ^Pullies and their Ropes reprefented by the $th, jthj, 
and 8th Figures are call'd Tackles of Four* Tackles, of Five^ 
and Tackles of fix. 

40. The Machine reprefented in Fig. 6. is the moft incon- 
venient for railing the Weight 6 ; but the moft convenient for 
bringing together the Ends of two Beams without danger of 

ben^ 



ACourfe of Experimental Phikfophy* t o r 



bending them, as if the Ends A and B were to be brought Left. III. 
together gradually. N.B. This Way of ufing Tullies is calPd^y^u 
lacing. 

41. We rauft obferve that the Rule abovementionM is only 
applicable to the Cafes in which the lower Puliies rife all to- 
gether in one Block with the Weight ; but when they a£t up- 
on one another, and the Weight is only , faftenM to the lo weft 
of them, the Force of the Power is very much encreafed, each 
Pulley doubling it. As for Example *, a Power whofe Intenfity* Pi. ioj- 
is equal to 8 ife (applied at a) will, by means of the lower Pul- Fi S- 9 - 
ley A, fuftain 16 tb * : A Power equal to 4 1fe (at b) will, by * 3 S*. 
means of a lower Pulley B, fuftain the Power of 8 ifc afting at 
a: A third Power equal to 2 ib (at c) will, by means of the 
Pulley C, fuftain the Power of 4 at k: A fourth Power of 

1 lb (at d) will, by means of the Pulley D, fuftain the Power of 

2 lb (at c) ; and this is not alter'd by having its Rope carried o- 

ver the upper Pulley or Roller E * ,N. B. What Weight ^ each* 37-- 
pulley and each Rope Bears in this Syfiem of gullies is fet dowm 
in the. Figure. 

Experiment XII. SP/. 10. Fig. 9. 

.A Weight of 16' ft. hanging at the Pulley A, (of the Machine 
Fig. v. made up of four fingly moveable Puliies, a Roller at E and 
four Hooks upon the Arm E F) let the little Weight 1, whicb 
keeps in JEquilibrio the Weight 16, be raifed up to k 16 Inches, 
high, and the Weight 16 will only defcend in the Line g fa 
an Inch long. This fhews the reciprocal Proportion, between 
the Weights and their Velocities to be applicable to this, as; 
well as to all other Cafes of Puliies, as may be known By 
moving the Weight or Power in any Combination of Puliies, 
and meafuring the Spaces which they go thro'. Thus in Fig. 4 * * Pi. u». 
while 2 goes down to a, 1 goes up to B,, juft twice as far, F 'g- 4»- 
&'c* This Proportion therefore will always- produce an JEqui-* Ann. 
librium in this as well as in all other Mechanical Engines-, 

N. B. The Ropes j afcending and defcendingj are always to* &e 
fuppos'd parallel, except where it is otherwije exprefs y d % and* Aon; im 
in every Figure reprefentingTuUies J jhe ( Power " and height ah' 
marked with the Letters P and "Wi 







a. M wwye g 

OfthrMXLBin 

Ce£t. III. 42. When a Power by help of a Rope, or any other Means, 
v^'"V^ V ^ the Circumference bf a Wheel as to caufe the 

laid Wheel together with its Axle to rum round and raife a 
Weight applied to the Axle in any Manner, fuch a Machine is 

* PL -10. ca lfd ah Mete in the Wheel j or Axis in Teritrdrhid *. 

Fig. 10,11. Since in this Instrument the Wheel and its Axis move to- 
gether ; it is evident, that in one Turn of the Wheel, when the 

* Plate 10. Power *P defcends a Length equal to the Circumference of the 
Fig. rb. wheel, tile Weight W rifes an Height equal to the Circumfe- 
rence of the Axis A by the winding of the Rope which carries 
the Weight upon the faid Axis, And fince, when there is an 
Mquiltbrium between two Weights as W and P, there mull 
be a reciprocal Proportion between their Mafles and Velocities ; 
W will be to P, as the Circumference of the Wheel to that of 
the Axis (fuppofing the Rope bf no Thicknefs) or as the Semi- 
diameter ot the Wheel tb the Senlidiafneter of the Axis (that is 

* Plate io. as * D K to K A) becaufe the Semidiameters of different Circles 
Fig. 11. are in the fame Proportion to one another as the Circum- 

fcrcnccs. ^ / 

Hence it follows, that the lefs the Axle is in Proportion to 

the Wheel, the greater may the Weight be, which is fuftain'd 

or rais'd by the Power. 

EX PE RI jaen t XIII. TL 10. Fig. to. 

42. The Machine reprefented by the Figure is a Model (made 

by a Scale of an Inch to a Foot) of fuch an Axle and Wheel as 

is often made ufe of to draw Water out of a Well, by means 

of a Ppwer drawing by a Rope applied to the Circumference 

of 6he of the Wheels of the Machine, [or by preffing down 

fuceefevely the Handles £, F, G, H, I, K, whilft another Rope 

or Chain is wound up upon the Axis A or B, a Bucket hang- 

ing at it ihffead of the Weight W. Here in the Experiment one 

'Pound hanging at the Circumference of the biggeft Wheel C D 

will keep in Mquilibrio 12 Pounds hanging at the fmalleft 

Axis A, or 6 Pounds at the Axis B, and only 3 Pounds upon the 

Circumference T V. In the fame manner, when the Weight 

Banging at the Axis continues in the fame Place, and to be of 
0 the 



jt Cmxrfe of Experimental WW&jfhphy. 103 

the lame Quantity, viz. 12 Pounds, then ;he Power which, fte&m 

, } : _r \xn, QO i r- ; c fi nna1 to .1 Pound. 



muft be equal to I | Pound, if it be applied at S R ; but ir it be 
applied at any of the Handles at the Diftance of ? of an Inch 
from the Circumference of the Wheel C P (which is the fame 
as if a new Wheel was added of f an Inch more in Diameter) 
then a Power equal to no more than H of a Pound, will keep 
the Weight in Mquilibrio ; md raife it, if its Intenhty be en. 

creas'd ever fo little. . r . , , , tr • Ut . 

This is more clearly reprefented in Fig. Ji. where the Weights * pi ate i 
are reprefented by the Letters W,w,< and the Powers .by the Fig. u. 
Letters P,/, », and where you muft obierve, that unlets the 
Power ads upon the Handles abovemention d at right Angles, 
or in the Lines E tt, F f, or G g, ®c. the &kg cannot _ be the 
fame as making ufe of a new Wheel E, B, G, H, to which the 
Lines E tt, f f, and G g are Tangents. 

44 . Tor. if a Power, as for Exapple, P, : ags. obliquely up- 
on any of the Handles, as in the acute Angle V* K, or ■its cor- 
refpondently obtafe Angle PJK, the Line of Predion of the 
faid Power * becomes the Tangent of the Circumference D Ci * Ann. 
and .confequentty the Pow&r ads as if it drew by a Rope ^o- 
ing round the Wheel C D : And if the pbiiquity was grater 
as when the Power / draws the handle G in the Angle P G K, 
the ErTea will be no greater than if the faid Power ihould draw 
bv a Rope going round the Circumference S R. The Powers 
in thefe Cafes muft be encreasM in the fame Proportion as the 
Lines D K and S K are fhprter than Ef See the Numbers, 
in the Figure, which exprefs the Intenfities of the Towers 

N B. We have taken no Notice here of the Thicknefs of the 
Rope, to which a Regard is to be badmTrapi.ce, always 4 jd-- 
dinz half the Thicknefs of the Rope to the Sewdtameter tf the- 
Axis: And if the Rope is wound up upon ft fW, for every fuch 
Turn we md ft ill add half its Thicknefs, which js the R0W 
wh more Tower mufi be .applied when the Axis is thus thick* 
ned 3 as often happens in drawing Water from 4 deef and nar* 
row Welly over which we cannot have a long Axis. 

a< If the Rope to which the Power is faften'd be fuccef- 
fivelV applied to different Wheels, whole Diameters are bigger 
and bigger, the Axis will continually be turn'd with more eafe, 



7 



194 ACourfe \oj \ Experimental TUlofophy. 

J2@a. IILunlefs the lntenfity of the Power.be diminifh'd in the fame Pro- 
portion ; and if fo, the Axis will always be drawn with the fame 
Strength by a Power continually diminifhing. This is praais'd 
in Spring-Clocks and Watches, where the Spiral Spring S, which 
is ftrongeft in its Action iwhen firft woundup, draws the 
Fuzee F, or continued Axis in Teritrochio by the fmalleft Wheels 
near B ; and as it unbends and grows weak, draws at the lar- 
ger Wheejs near A, in fuch manner that the Watch-work is al- 

* Plate io. W ays carried round with the fame Force *. 

* ie. 12- 



% 46. A s Leavers and Pullies afting upon oi»e another are fome- 
times joyn d together to encreafe the Adion of the Power 
whereby it may fuftain or lift a greater Weight ; fo it is ufua! 
to make a compound Axis in Teritrochio by combining together 
two or more of thefe Machines. Becaufe tho' by means of a 
long Axle capable of receiving a great deal of Rope, one may draw 
Weights from a great Depth ; yet, as a very fmaU Axis would be 
too weak for very great Weights, or a large Wheel would be 
very coftly, if fufficiently ftrong, or make a cumberfome En- 
gine which would take up too much room ; it is more ad- 
vifeable to combine Wheels and Axles, by means of Pinions oi- 
lman Wheels upon the Axles, whofe Leaves (or Teeth) take 
hold of Teeth made in the large Wheels, as we fee in Clocks 
* », which have feyeral Axles and Wheels, or fome fort of Cranes 
03 » »3. which have only two of them combin'd together. 

Experiment XIII. SP/. ic. Fig. 13. 

. 47* This Machine confifts of two Wheels with their Axles 
the farft of which A B C (on whofe Circumference A B is coil'd 
the Rope which carries the Power P, which is a Weight 
of one Pound) has a Pinion of eight Teeth on its Axis at C 
which takes the Teeth of the Wheel F G of the other Axis in 
Terttroctno The Wheel F G has forty Teeth, and its Axis 
H K is in Diameter the eighth Part of the Wheel A B. Hans 
the Weight W of 40 ft U pon the Axis H K, and it will be 
kept m Mqutltbrio by the Power P, which is equal but to 

1 ID* 

*. F we LfrPPofe the Axis C I of the fame Diameter as the 

w » V\ " - S eVlde f V hat the Power P would have fuftain'd 
Jwt H * hanging on the faid Axis ; nor would it have fuftain'd 



more 



A Courfe of Experimental Philofophy. 105 

more on the Axis K H if this laft Axis had gone round as of- Let IIT 
ten as the firft Wheel AB (which would have happeh'd if the ,/ynj' 
Wheel FG had had no more Teeth than the Pinion C) but Platei °- 
fince its Wheel has five times more Teeth than the Pinion on F ' 8 I3 ' 
the Axis C I, it muft go five times flower than the faid Axis- 
and confequently. the Weight W goes up five times flower than 
it would have done on the Axis CI; therefore it has forty times 
lefs Velocity than the Power P, rifing only one Inch whilft P 
defcends forty. 

Hence it follows that the Ratio of the Power to the Weight 
is compounded of the Ratio of the Diameter of the Axis of 
the laft Wheel (where the Weight hangs) to the Diameter of 
the firft Wheel (where the Power is applied) and the Ratio of 
the Number of Revolutions of the laft Wheel, to the Number 
of Revolutions of the firft Wheel in the fame Time. As for 
example, here the firft Ratio is of i to 8, and the laft Ratio 
is of i to 5 ; therefore the Ratio of the Power to the Weight 
is as i to 40, viz. the Compofition or Multiplication of thofe 
two Ratios, becaufe 5x8 - 40. And this holds good> let the 
Machine conjift of ever fo many Wheels. 

Of the Inclined T L A N E. 

m 48. For the better underftanding the Ufe of the inclin'd Plane 
in Mechanicks, we muft remember what has been faid before 
concerning the Velocity of a Weight * viz. that whatever* Ann.*. 
Line the IV eight defcrtbes tn its Afient by the Attion of the Tower Le6t - 2 - 
we are to call its Velocity only that Line which reprefents its 
perpendicular Afient or T>efcent. 

If it fhould be requir'd to lift up a very heavy Body as W 
or w * the Height C B, it would be impracticable to raife it up* Plate 10 
m the Line C B without a Power whofe Intenfity is equal to Fig. 14. 
that of the Weight; and even in that Cafe very inconvenient 
to do it, efpecially in building. But if an inclin'd Plane AB be 
laid raifingfrom the horizontal Line A C, from whence the Weight 
is to be raifed, a lefs Power than the Weight will ferve for 
that Purpofe, unlefs it puflies the Body direftly againft the Plane 
(as in the Direftion W T) or draws the Body away from the 
Plane (as from W towards e, t, or L, or) in any Direction on that 
fide of the Line E e *. * Ann. u. 

r 49* 1 HE 



io6 A Omrfe of Experimental Phihfophy. 



Left. III. 49- The Direction in which the Body can moft eafily be 
drawn or pufh'd up the Plane (as in driving a Wheel-barrow) 

Plate n. j s j n t ij e Line W w M, parallel to the Plane and paffing thro* 
Ig ' I4 ' the Center of the Weight; for whether the Power drives a 
Plane k K (in a Direction perpendicular to it) along the Line 
W M, or the Power P (by its Defcent to />) draws it in the 
fame Line, the Velocity of the Power will be equal to the 
Line W w, the Space defcrib'd by the Center of Gravity of 
the Weight, whilft the faid Weight rifes only the perpendicular 
Height Z B (z=m W) or has the faid Line properly to exprefs its 
Velocity. If the Body was a Cylinder, as a rolling Stone, and 
the Plane T t were to pafs thro' the Gudgeons or Axis of 
the faid Stone; it is evident that the Cafe would be the fame; 
and as the Weight P has its Rope running over the Roller (or 
upper Pulley ) M, the Line P p will be the Velocity of the 
Power. Therefore in this Cafe the Weight (if kept in JEquili- 
brio) be to the Power as W w (=r T B) to w Y (— B Z) 
or as the Hypotenufe A B is to the Perpendicular B C, which 
(by Eucl. 4. 6.) are in the fame Proportion ; and consequently if 
the Power be ever fo little enereas'd, it will draw the Weight 
up the Plane. 

N. B. In Traffice the Tower muft be pretty much encreas'd 
if the Body is not fmooth and fpherical or cylindrickj and the 
Tlane very fmooth. But as all forts of Bodies are to be drawn 
up j to reduce them as near as we can to a Sphere or Cylinder v, we 
muft j aft en Wheels to them* or (which is the fame Thing) lay 'them 
on a Wheel-Carriage. 

50. That the Power acts with the greateft Advantage, 
whilft it draws in the Line of Direction W w (parallel to the 
Plane) is evident ; becaufe if one End of the faid Line of Direc- 
tion remaining ftVd at W, the other fhould move towards B, or 
beyond k, then the Body would be partly drawn againft the 
Plane, and therefore the Power muft be encreafed in Propor- 
tion to the greater Difficulty of Tradion : And if the End w of 
the Line abovemention'd fhould be carried to D, or beyond it, 
the Power muft be alfo encreafed in as much as it endeavours 
to lift the Body off from the Plane, How much the Tower muft 

be 



A Courfe of Experimental Philofiphy, 1 07 

be encreafed in Proportion to the Angle, which its Line of ©/-Led. III. 
reSiion wakes with the T lane ^ will be jhe.wn in the Notes*. o^V-xJ" 

* Ann. 11. 

51. If the Power draws in a Line of Direction W B, paral-pi ate 10 
lei to the Bafe of the Plane ; then in order to keep the Weight Fig. 14. 
W in JEquilibrio by the Power 17 ; the faid Power mull: be & to 

the Weight ; as Z B to Z T, or as the Perpendicular B C to the 
Bafe A C of the Triangle A C B. For if we fuppofe the Pulley 
R at fo great a Diftance from W, that the Line of Direction 
W R may not fenfibty alter its horizontal Pofition, whilft the 
Body W rifes the Height B Z, then will the Power n defcend 
to whilst W rifes the Height B Z, in fuch manner that n ^ 
(— W Y, and not W w) will be the Velocity of the Power. So 
that the Velocity of the Power to that of the Weight will not 
be as the Hypotenufe to the Perpendicular, as in the former Cafe 
but as the Bafe to the Perpendicular in the Triangle A C B. ' 

Ie the Power be encreafed juft enough to overcome the Fric- 
tion of the Plane and draw up the Body W, let the Pulley R 
be lifted up gradually to r, fo as to keep the Line W R paral- 
lel to itfelf till it comes to w r, and the Power will be defend- 
ed to t when the Weight is come to wB. But n ir together 
with the Diftance R r, is equal to n ^, or W Y, &c. And this 
Traction being conftantly ' made in the Angle WBT, is the 
Cafe 

Of the W ET> G E. 

52. The Wedge is a fhort triangular Prifm, whole two op- 
pofite and parallel Planes are re&angular Triangles, fuch as the 
Section ABC*,- the reft being rectangular Parallelograms ; the * Plate 10. 
Edge or entring Part of the Wedge is made by the meeting of Fi S-u. 
two Planes in whofe Section is the Point A, and the Back of it is 

the Plane oppofite to the Edge, on which the Hammer or Mal- 
let ftrikes to drive the Wedge forwards. The Reprefentation 
of it is feen in the Figure A B C D E *. * Plate n. 

, If upon the horizontal Line AC* produc'd towards p, heVt*' la 
laid the Weight w at the Point d, and a Plane as Gg to ftop itFig 14 
from going towards A, whilft the Wedge A BC is pufh'd un- 
der it from /towards A ; as the Wedge is driven from C to A 
the whole Length of its Bafe A C, the Weights rifes juft the' 

P 2 Height 



1 08 A Courfe of Experimental Vhilojh$y. 

Left. III. Height CB, or the Thicknefs of the Wedge : TBereforr tfie 
v^v^ Power will be to the Weight, as B C to A C\ 

55. The Proportion of Force usM would he juft the fame if 
a Plane as F/ were to move parallel to it felf, and perpendicu- 
lar to A C, and pufh^up the Weight, as W, from A to B along 
the Wedge fuppos'd then immoveable. Nay, it would be the 
fame if the Weight was only pufh'd from one part of the Wedge 
to another, the Plane moving but from Yf to Ggj or (which 
is the fame) from E e to D d^ for then w Y would exprefs the 
Rife of the Center of Gravity (or the Velocity) of the Weight, 
*and W Y the Velocity of the Power, which are ftill in the Ratio 
of B C to C A. 

This is the fecond Cafe we mentioned concerning the inclined 
Plane, and may be confirmed by the following 

Experiment XI V, Tl. 11. Fig. 2. 

* Plate xx v 54. Take the Machine defcribM in the Figure, in which the 
Fig. a. fmooth Plane or Board B A H I, moveable on Hinges at B and I, 
may be raifed fo as to make any Angle with the horizontal 
Board NLBI, by help of the Quadrant D, and fixM in its 
Pofition by meaps of the Screw at T ; and having made faft 
the Head D E in the Groove S s by a Nut under the hori- 
zontal Board, raife the Pulley C of the Arm D C 3 fo that a 
Line going over the faid Fully in the Direftion C M, may be 
parallel to the Plane A B. Then take a little wooden Cylinder 
M, the Ends of whofe Axis or Pivots go thro' a brafs Frame, 
as at fo that it may be drawn eafily by a String fix'd at M; 
and lay on the faid Cylinder upon the inclined Plane, having 
faftenM to M a String which goes over the Pulley c and is 
joyn'd to the Ball P, which being made ufe of as a Power will 
fuilain the Cylindrick Weight M, when P is to Mas AC the 
Height of the Plane, to A B its Length. A little: more Weight 
added to P makes it draw up the Cylinder. 

But if the Arm E C be lower'd, fo as to come into the Pofition 
E G, / mull: be to M (in order to keep it in Mquilibrid) as A C 
the Height of the Plane, to C B its Bafe. N. B. Here it is to 
be obferv'dlhat tho' the Addition of a little Weight to p will 
make it begin to draw the Cylinder M up the T lane ; that the 
Cylinder will not be drawn quite up by the T>efcent of $ 9 be- 

caufk 



A Courfe of Expermeffl^ 



10^ 



ianfe the Angle which the Line of 'Direffiim of the Tower makeslL&Qt. HE 
with the T lane will be encreafed as the Cylinder rifesup ; but^^^TSJ 
if the Tulky G be gradually lifted up to K, whilfi the Cylinder 
is drawn up to m, the Tower ^ which then will be at ir^ will 
have the fame EjfeEl on the Weight at m, as It had before at M r 
&c. and the Weight (when kept in Mquilibrio m the Line of 
^DireSiion M G or m K) will fill be to the Tower as M n to n m, 
^ B C toC'A. 

Th i s Machine alio experimentally fhews the Effe£t of the Pow- 
er^ whatever Angle its Line of Dire&ion makes with the Plane. 

55. The Wedge, which we have hitherto confider'd, is a 
Wedge a£Hng in the moft fimple manner, only with one of its 
Surfaces; for when it Aides upon the Plane G A * to lift the* PL io 0 / 
Weight W, it does only a£t with its Surface A B, the Surfaced- l ^ 
A C only applying it felf to the Line A p\> without removing it 

from its Place, Thus if a Moulding was to be fepa rated from 
a Wainfcot as Mm * from W w by Means of the Wedge* PIate m 
A CB, it is plain that a A the Velocity of the Wedge Fig, 
(fo far as it is driven in, when from the Pofition a b c it comes 
into the Pofition ABC) wou'd be to a m the Velocity of the 
Moulding as AC to B C. Therefore, &c. So it would be if 
a Pillar Handing upon a Floor was to be raifed up without 
moving the Floor. 

56. But in the common way of ufing the Wedge , both* 
Sides of it a£t> as in cleaving Wood : Then the Proportion of 
the Power and Weight are different from the former ; fort-hen* 
the Power will be to the Weight as half the Wedge's Thick- 
nefs to its Length. But then, we may eafily reduce this to 
what has been faid before ; hecaufe here we make ufe of a dou- 
ble Wedge. For let us fuppofe C a* an immoveable Plane, * Pfate ml 
and on each Side of it a Wedge, as B C A and £ C A, made F, S° ^ 
ufe of to remove a Weight as c or d from the faid Plane ; the 

Power pufhing the Wedge will be to the Weight but as c C (= A c 
— B C) or d D (- = A D = C b) to the Length of the double 
Wedge C B A b y which is now got to A c a d, Some Mechanical 
Writers have miftaken this Cafe by adding together the Tingle* 
Velocities of c and d, vi&. C c ■•+- d D, and calling that Sum the 5 
Velocity of the Weight, which they comparM with A a the 
Velocity of the Power y but we muft confider that if the two 

Bodies^ 



vm A 1 Comfi. of Experimental Phihfophy. 

OLe.£t. III. Bodies to be Eemov'd from each other (as the Parts of the 
.v^v^v-- Wood to be cloven ) were laid upon one another on , either 
Side, as for example at dj their Velocity would only htdD r and 
they would be removM as eafily then by one Wedge as b C A, 
from d to D, as by the two Wedges in the former Cafe. For 
th(P in conjidering the Momentum of Bodies j the Sum of the 
Momenta of all the Tarts is to be taken for the Momentum 0/T 
the Whole ; we are not to take the Sum of the Velocity of the 
Tarts for the Velocity of the whole j but only the Velocity of the 
Center of Gravity of the Body, when we confider how far it is 
removed out of its 'Place. If a Leaver or Balance was made 
* Plate ii. like a Fork and the Part C A was jujl double of either of 
5- the Tarts of the Fork as C B or CD, and the Center of Mo- 
tion fix* d at C; it is evident that one Pound at A will keep in 
iEquilibrio two Pounds at the forked Endj tho' the Pounds 
were to hang Jingle * a two Pound IV eight being always equi- 
valent to two Jingle Pounds / but if the Sum of the Velocities 
of B and D were to be taken j there mujt then be two Pounds 
•at A to fujlain the Weights at B and D, the Radius C A giv- 
ing no more Velocity to the \ Weight at A, than the Radius 
C B or C D, of half its length „ to the Weights at its Ends, 
which is abfur*d^ &c - 

57. In both Cafes of the Wedge, it is not only necefTary to apply 
a Force fomething greater than either in Proportion of the half 
Thicknefs or of the whole Thicknefs of the Wedge to its Length, 
that the Power may overcome the Weight ; but becaufe the Sur- 
faces even of the moft polifh'd Wedge are very rough (in Compa- 
rifon to the Mathematical Smoothnefs which we have fuppos'd) 
and the Bodies to be feparated likewife very far from having 
their Surfaces truly plane; we muft make ufe of an additional 
Force , to overcome the Stickage arifing from that Roughnefs. 

This Fri£Uon or Stickage, which is not great in other Engines, 
is very confiderable in the Wedge, Experience fhewing that a , 
Wedge laden with a vaft Weight, has hardly any EffeQ:, efpeci- 
ally in cleaving Wood; becaufe not only the Surfaces of the 
Wedge, as was faid before, but the Parts of the Wood to be 
cloven are always rough, and fo clofe, that their Fridion very 
much hinders the Motion; which Obftacle we endeavour to re- 
move by Percuffion, which here is of wonderful Ufe ; for Expe- 
rience fhews, that a Blow upon the Head of a Wedge, makes it 

enter 




enter eafily into a hard Body ; the Reafon of which feems to be, Left. HE. 
that a Blow, by putting all the Parts of the Wood in motion, v^vN-/ 
makes them tremble and be difunited, fo as to leflen the Stickage, 
and facilitate the Motion of the Wedge, The Effed of Percuffion 
will be greater in Proportion as the percutient Body is heavier and 
moves fwifter. 

Tlate ii # Fig. 6* 

58. To prove by Experiments what has been faid of the Wedge r 
we fliuft make ufe of the Machine reprefented in the 6th Figure 
of Tlate 1 r . 

A BCD is a Brafs Frame, confifting of two horizontal Pieces* 
AB and CD, and two vertical ones AD and BC, {landing upon,, 
and fix'd to the former, each of thefe laft Pieces has on the In fide 
about the middle, two little PulliesNO, P Q^not exa£Hy in the 
fame Plane, left the String that goes over the one fhould fall foul ; 
upon the String which goes over the other. EF, GH are two 
Cylinders with Steel Axes, which are brought together (their Axes 
rolling on the Vertical Pieces) by the Defcent of the Weights 
RS, each of which is divided into two Parts, by means of its Pulley 
T or V, fo as to draw the Cylinders equally towards one another,, 
by the Strings and Brafs Loops T N H, and t Y j, and two fuch 
other Loops at the other End of the Axis of the Cylinders. That 
the Cylinders may come clofe together, without touching the 
Pulleys N, O, P, Q., the Plates at their Bafis (which are a pretty 
deal larger than the Cylinders) are made convex towards the 
Ends of the Axis. The two Plates ZM, ZM, juft wide enough 
to apply themfelves to the Cylinders, without rubbing again the 
Plates at their Ends, are join'd at M in the Manner of an Hinge,, 
fo as to make a Wedge, and be open'd to any Angle meafur'd by 
the graduated Arc I K L, which paffing thro* the Plate,, holds/ 
them faft, by means of the two little Screws Z, Z, X is one of 
two bended Wires, whofe Ends being flipp'd into two Holes,, 
keep the Cylinder EF from coming out of its Place, and only 
allow it to turn upon its Axis, when the Loop P (and its oppo- 
fite under E) is carried over the Pulley Y (and the contrary Way) to* 
the Axis of the other Cylinder at/, when only this laft Cylin- 
der HG is to be puflh'd away by the Defcent of the Wedge, which 
by its own Weight, or the Addition of the Weight W, feparates 
©ne Cylinder from the. otlier,, which is fix'd (when the pricks 



1 1 1 ACourJe of Experimental Philofophy. 

Le£tXII.Line reprefents the String) or removes them from each other, 
wo^w (when Y ^ reprefents one String, and H N the other.) 

Eyperiment XV. 

59. Every thing being in the Pofition reprefented in the Fi« 
* Plate 11. gure open the Wedge to any Angle at Pleafurej as for Ex- 
Fig, ample, to an Angle of 20 Degrees, and hang on fuch a Weight W, 

as may, together with the Weight of the Wedge, draw down the 
Wedge, and, by feparating the Cylinders, raife the Weights R andS. 
Open the Wedge to an Angle of 40 Degrees, and twice the Weight 
will be required to bring down the Wedge ; but if you flip on 
the Wires, fuch as X, to nx the Cylinder E F, and hang the four 
Loops and Strings upon the Cylinder HG, the Wedge atting only 
with one Surface to remove the Cylinder HG, will require twice 
the Weight to bring it down, that it would if it afted with both 
Surfaces; that is, being openM to an Angle of 20 Degrees, as much 
Force will be required to bring it down, when only one Cylinder is 
moveable (tho 1 the other can freely turn about its Axis) as if it 
was open'd to an Angle of 40 Degrees, and both Cylinders 
moveable. 

Of the Screw. 

60. A Screw is a Cylinder cut into feverat concave" Surfaces, 
or rather a Channel or Groove made in a Cylinder, by carrying 
on two fpirai Planes the whole Length of the Screw, in fuch 
manner that they may be always equally inclined to the Axis 
of the Cylinder in their whole Progrefs, and alfo always inclined 
to the Bafe of it in the fame Angle. 

The Screw may be alfo confiderM as a Wedge carried round 
a Cylinder, which in that Cafe is call'd the Arbor of the Screw, 
the Wedge fo carried on making what is calPd the Thread 
of the Screw, as may be feen in the 7th, 8th, 9th, 10th and nth 
'* Plate 11. Figures *: The Arbor of the Screw being A B in Fig.j^ and 
Ffe. 7,8, 9, a c b d in Fig. 8- as if the Cylinder A C B D was infcrib'd 
t0 * within the Screw. 

In the 8th Figure we may fee the manner how a Screw is 
made, if it be cut out of the Cylinder PHIQ^ then H K L 
M NOP is a fpirai Line going about the Cylinder, marking the 
prominent Part to be left of the laid Cylinder, and hklmno, the 

Line 



A Courfe of Experimental Philofophy. n q 

Line marking the Depth to which the Screw is to be cut Left. Ill 
(fuppofing the fame Line to go round the inner Cylinder or 
Arbor A B C D, tho' not exprefs'd here to avoid Confufion) Plate n . 
and then b L /, / N &c. will reprefent the prominent Part Fig. 8. 
or Thread of the Screw. Now, if inftead of cutting the Hol- 
lows H h L, L / N, N n P, &c. into the Cylinder PHIQ^a 
continued Wedge be fix'd to a fmaller Cylinder as ACBD, 
or rather a c b d J the fame kind of Screw will be made, and 
abed will be the Arbor of that Screw. Sometimes the' moft 
prominent Part of the Thread, as L, N, &c. is not fliarp but 
flat, and then the Thread is caU'd a fquare Thread, as in Fig. 1 1 . 
which reprefents the Seclion of fuch a Screw. This fort of 
Thread is not us'd in Wood, but in Iron and other Metals it 
is of good Service, being commonly more durable, and raifing 
the Weight with more eafe than the fharp Thread, as will be 
more fully fliewn in the Notes *. * Ann. is. 

Of the Force of the SCREW. 

To make an Eftimate of the Force of the Screw (which may 
be compar'd either to an inclin'd Plane (as we have confider'd 
it among the mechanical Powers) or to a Wedge, according as 
its Arbor does or does not advance in a progrefTive Motion 
whilit it turns round its Axis to raife or flop a Weight or 
to prefs Bodies together, which are the feveral Ufes of a Screw) 
let us take a flexible Wedge, as for Example one of Paper, and 
coil it round a Cylinder * as is reprefented in the Figure, where* Plate 
A B is the Arbor, C I D one Thread or Helix, D H E ano-F'g. 7- 
ther , and E F G Part of the Wedge left to fhew the Pro- 
portion between the Power that turns the Screw and the 
Weight W. 

63. If the Weight is pufh'd up the Wedge (or which is 
the fame, rais'd perpendicularly by the Wedge flipping under it) 
from F to H in the Direaion W w, then will H G be the Ve- 
locity of the Weight, and G F the Velocity of the Power, which 
is the Cafe of the inclin'd Plane becoming a Wedge ; and this 
will be the Analogy for the Screw * thus afting. * 5 ,. 



As 



ii4 A Courfe of Experimental Phtt(fvpby 



Le£t-ITL As a Circle whofe Diameter is Kb: 
l/YV To HI the Diftance of two Threads : : (or as the Bafe 

F G : to the Perpendicular H G ; :) 
So is the Weight : : 

To the Power applied to the Arbor at A to raife a 
Weight up the Thread H D I C. 

N. B. We fup^ofe the Diameter of the Arbor at A, and of 
the Screw at H nearly equal. 
Plate if. This is the Cafe or the loth tig. where the moveable Plank 
Flg * ,0e D K is carried down by turning round the Heads G, G, of 
the Screws A B and C D, in order, to prefs ftrongly the Bo- 
dies placed between the Planks D K and M L, whilft the Piece 
HI fix'd on the upper Plank is either guided thro' an Hole, 
or being only lookM at, ferves to fhew whether the Plank 
K D be brought down horizontally as the Screws are turned. 
When long Leavers are thruft into the fquare Holes at the 
Heads of the Screws, the Force of the Screw is much en- 
creafed, and then the Weight : will be to the Power : : as the 
Circumference of the Circle defcribM by that Part of the Lea- 
ver to which the Hand is applied : to the Diftance between 
£j ate "' two Threads. So in Fig. 13. .as the Circumference of the Cir- 
Ig * * 3, cle whofe Radius is A H to C c the Diftance of two Threads 
of the endlefs Screw C D :: fo is the Refiftance of the Teeth 
of the Wheel I: to the Power applied at H. 

* P1. 11. 64. But if the Weight W * be driven along on the Wedge 
Fl S- 7' H F G in the Direction W w parallel to the Surface of the 

Wedge, then will this Cafe be the fame as that of the inclined 
* 49. Plane *, and therefore the Analogy for the Screw in the Progref- 
fion of it will be, 

* Plate 11. As the Spiral-Line H D I : * 

Fi &- 7 * To HI the Diftance of two Threads :: (or as the Hy* 

potenufe F H : to the Perpendicular H G) : : 
So is the Weight : 

To the Power apply'd to the Arbor at A in a Spiral Di- 
rection parallel to H D I C. , 

Tfl £ 



A Courfe of Experimental PMlofophy. 1 1 5 

The 9th Figure reprefents the Practice of this, whether the Left. Ill, 
Female Screw D E be brought down on the Male Screw to- 
wards the Plank B, or the Plank B and its Screw be brought p late lle 
up toward D E by {brewing its Screw up higher into the Box * s ' 9 ° 
or Nut D E. Therefore when Handles as D and E are us'd to 
encreafe the Force, The Weight will be to the Power : : as the 
fpiral Circumference defcrib'd in one Revolution by their Ends 
to which the Power is apply'd : to the Difkmce between two 
Threads of the Screw. 

This Cafe is applicable in Practice to the Screw at the End 
of Gimblets to facilitate the boring of Wood; to the bringing 
down the Nuts in large cold Prelfes, and to the common Ufe 
of Screw-pins for holding together the Parts of Machines, 

The greateft Part of Mechanical Writers have only taken 
Notice of this laft Proportion of the Force of the Screw. 

6$. THo r in the Theory, if the Product of the Intenfity of 
the Power into its Velocity does ever fo little exceed the Pro- 
duct of the Weight into its Velocity, the Power muft raife the 
Weight ; yet here the Power, or its Velocity, mult be fenfibly 
encreafed to produce this Effe£fc in Practice by Reafon of the 
great Fridion in the Screw, which is the fame that we have 
taken Notice of in the Wedge; only we are to obferve that 
there is more Fri&ion in the fharp than the fquare Thread, 
which may appear by a Sight of the 14th Figure*, where* Pi. n. 
B A C D reprefents the Sedtion of a fquare Thread, and b a d^ H>- 
the Seftion of a fharp Thread. As the Part A C does not touch 
the Female Screw, which only bears with its Force and Weight 
upon the Flat A B, the Line AS in the fquare Thread com- 
pared with a h in the fharp Thread (on which Part the Female 
Screw bears) will fhew the Fri&ion to be lefs on the fquare 
Thread in Proportion to thofe Lines, befides the Obliquity to be 
confider'd elfewhere *. * Ann. 13. 

66. The Difadvantage to the Force of the Power occafion'd 
by the great Friftion in the Screw is fully recompensed in the 
Ufe of that Machine ; becaufe, on that Account, the Screw con- 
tinues to fuftain the Weight even after the Power is removed, or 
ceafes to ad, or to prefs the Bodies again ft which the Power 
had driven it ; whereas in the Balance and Leaver and other 
mechanical Powers, the Weight ceafes to be fuftain'd and goes 

2 back 



i\6 A Courfe of Experimental Vhilofophy. 

Left Ill-back when the Power ceafes to aft. The Reafon of this is, that 
AXVV> Weights when they are rais'd by Screws endeavour to defcend 
perpendicularly, whereas the Screw has been pufhM againfl: them 
very obliquely, fo that it can only be pulh'd back again in that 
oblique Direction, which cannot be given to them by the Gra^ 
vity of the Weight tending downwards, if there be the leaft 
Fri&ion againfl: the Thread of the Screw: So likewife when a 
Body is prefsM by a Screw, its Surface fe-a£ts in Lines perpen- 
dicular to it, that is in the Dire&ion of the Arbor of the Screw, 
whereas the Screw cannot be driven back unlefs it be movM 
in the Dire&ion of its Thread, which makes a great Angle with 

* Plate ii. the Axis of the Arbor. Thus the * Plank K k Fig. to. cannot 
Fig. 10. f a |] ^ own ] n the Dire&ion of its Gravity towards M L, un- 
lefs it could caufe the Screws to move in the Dire&ion Bb 

* Plate ii. or. D d. Neither can the Teeth of the Wheel I.-* Fig. 13. 
^g i3- preffing againfl: the Screw Cf D in the Dire&ion CB move 

the Screw or caufe the Handle H to move in the Direction of 
the Circle whofe Radius is A H, tho' the Power which went 
round in that Circle be remov'd, and the great Weight W does 
very flrongly endeavour by the Axis E F to mxn the Wheel I. 

Hence appears the great Ufe of the Machine of Fig. 10. 
which by Means of the ftrong Piece I may fupport the Side 
of an Houfe, and feveral of them applied in different Parts can 
fuftain a whole Building whilfl: the Foundation is mended or 
renewed. 

67: Whether the Screw be confider'd as a Wedge or an 
inclined Plane, it follows from what has been faid, that the 
clofer /the Thread of the Screw is, the greater is its Force 5 
and the more advantageous the Fri&ion ; the Power bringing 
forward the Screw with moft eafe, and the Difficulty to pufh 
back the Screw becoming the greater. 

68. As Percuflion is ufeful in the Wedge to leffen Fri&ion; 
fo in fome Cafes there is a kind of Percuffion ufed to drive on 
a Screw, as in Trintingj Coining and Sealing Inftruments with 
large Seals where a great Preflure is required ; and that is done 
by a Fly, which is a Balance going thro' the Arbor of the 
Screw and loaded with Weights at its Ends, or fometimes only 
one Brachium of it, as in the Printing- Prefs. 

Here 



A Courfe of Experimental Pbilofophy. i 1 



Here* inftead of the Hammer. or Mallet, which comes oil Dp- Left, 
on the Back of the Wedge with an accelerated Motion in a 
circular Direction to drive it into the Wood ; the Weight of 
the Fly comes down alfo with an accelerated Motion, but on 
an inclin'd fpiral Plane, and thereby having overcome the Fric- 
tion of the Threads of the Screw as it defcends , pufhes the 
End of it with great Force againft the Bodies to be prefs'd. 
But this will be further explained hereafter in another Lefftire. 

6y. The Friftion of a Screw joinM by a Fly is often made 
ufe of to regulate Motion by retarding a Weight which would 
defcend too faft, reducing the accelerated Motion of an heavy 
Body in its Defcent to one that is uniform, by deftroying juft 
as much Force as Gravity would fuper-add to the defcending 
Body in Motion. But we fhall explain this more fully when we 
fpeak of the Fall of Bodies. 

Tho' Balances, Leavers, Pullies, Axes in Teritrochio, and even 
Wedges can be made to aft: upon one another to encreafe the 
Force of the Power ( as has been fhewn in the Consideration 
of the Leaver, Pulley and Axis in Teritrochio.) Yet Screws can- 
not be applied to each other direftly, without the Intervention 
of fome other mechanical Power ; but in Compofition with o- 
ther mechanical Powers or fimple Machines, the Screw will ferve 
to make an Engine of vaft Force. Which leads me to the. Con- 
fideration of 

Compound ENGINE 

70. The Combination of two or more of the fimple Ma- 
chines, for the Ufes of Life (whether they be of the fame or 
of different Kinds) by means of a Frame of Wood or any Me- 
tal, makes what we call a compound Engine. As it would be 
endlefs to recount the feveral Sorts that are made ufe of, we 
fhall only give an Account of fome few, whereby we may 
judge of what may be performed by any Engine which has 
been made, or may be hereafter put in Execution, upon fight 
of an exaft; Draught of the intended compound Machine; that 
we may have a juft Value for what is or may be ufeful, and 
not be deceived by Pretenders to Perpetual Motions, and thofe 
who promife greater Effe&s by Machinery than is conformable 

to 



1 1 8 A Courfe of Experiment al P 





Left. IILto the reciprocal Proportion between the Xntenfides of .the Pow» 
^V^x^ers an d Weights of their Velocities 

* Ann. 14. 

Plated. 71. The two Machines reprefented in Fig. 1 and 2 of T late 6* 
Fig. 1, 2. reprefent the Scorpions which the Ancients ufed in War for 

* L. 2. throwing Stones, as I have defcrib'd them already*; I only 
Ann. 7. take Notice here, that they are compounded of a forked Lea- 
ver, two Axes inPeritrochio, and two Pullies, which laft in 
Fig. 1. only direfl: the Rope as they are Rollers, but double 
the Force of the Power in Fig. 2. 

Plate 7. 72. The Water Engine of 'Plate 7. Fig. 14 and 15 confifts 
Fig. 14, 15* of two Leavers E D and I K, and its Ufe is defcrib'd where it 
*L. 2. is firfl: mentioned 

Ann, 9. at 
tlic End 

73. The 14th Figure of Tlate 9. reprefents a Machine of 
great Force compounded of three Leavers acting upon one ano- 

* Plate 9. ther as defcrib'd above *. 

Fig. 14. / ' . 

\, 74. Tho' in the tenth /Plate, Fig. 4, ,5, 6, 7 and 8 the Ma- 
chines reprefented are made up of feveral fingle Pullies or 
Sheevers (Wheels moving round a Center-pin) like that of Fig. 1. 
yet as the fame Rope runs over or under them all, they muft 
be confiderM only as one Machine; for the Workmen call them 
by the fingle Name of a "Pulley or a Tair of Blocks *, and the 
Ancients confider'd a fingle or many Pulleys join'd in the man- 
ner reprefented in thole Figures \only as one Engine, which 
they calPd by various Names , according to its Number of 
Sheevers ; as Monopaftum when it had but one, 'Difpajlumyjhzn 
it had two, Trtfpajlum when three, Tetraffajlum when four, 
Pentafpajlum when five, and ufually Tolyfpafium when it had 
many Sheevers. 

* Plate 10. 75. But the Machine of Fig. 9 is a compound Engine ; 
Fi S- 9* becaufe in it the Pullies a£t upon each other and encreale the 

Force of the Power in a greater Proportion than according to 
the Number of Sheevers in the others abovementioxrd, as has 
* 41- been fhewn *. 



y6. The 



A Cowrfi yf Experimental PMlq/bphy. 



if 9 



76. The 13th -Fig. reprefents an Engine compounded 0fLe6t. HL 
two Axes in Teritrochio, whofe Operation has been defcrib'd *w/vn_^ 
md Force calculated *. * 47. 

77. The 9th and loth Figures of 'Plate 11 *, are compound * Plate u. 
Engines, becaufe fuch great Screws cannot be turn'd without Fig. 10. 
Leavers applied to them. N. B. It is to be obferv'd that when 

a Leaver or Leavers carry an Axis round, in which Cafe they 
are call'd Hand-fpikes or Bars , they perform the Office of a 
Wheel turning an Axis, and may therefore together with the 
Axis they turn be confider'd as an Axis in Peritroehio. 

This is more evident in obferving the Motion of the Han- 
dle A H of Fig. 13 *, made ufe of to carry round the Screw and* Plate \ U 
Axis A B. . Fig. 13. 

78. Because a Screw, which greatly adds to the Force of 
the Power, by reaforr of its Shortnefs, raifes the Weight but to 
a fmall Height ; and the Axis in Peritrochio (for the Reafons 
given in the Defcription of it *) tho' it may raife the Weight * 4<J.> 
to a very great Height, or from a great Depth, does not much 
encreafe the Force of the Power ; the Combination of thefe two 
Machines preferves the Advantages of each of them, and takes 

off their DefeQs : And this is done by caufing the Threads of the 
Screw C D to take hold of the oblique or skew Teeth of the Wheel 
as c, and by continually turning the Wheel round to draw up 
a great Weight as W by means of the Rope which is wound 
on the Axis E F. If on the Axis E F another Screw be added, 
as at G H, to turn afecond Wheel L, whofe Axis- M being of 
fufficient Length receives the Rope N inftead of the Axis K O, 
a much greater Weight may be raifed ; or an Engine of vaft 
Force may be made for boring hard Metals by means of cutting 
Inftruments fix'd on the End of the Axis M, or performing O- 
perations where much Strength is' requir'd. 

79. A Crane is an Inftrument of fuch general Ufe, that we 
cannot avoid giving its Defcription here. It is of two Kinds: 
in the firft, only the Gibbet moves upon its Axis, and in the 
fecond Kind call'd the Rat-tail' d Crane, the whole Crane with 
its Load, turns upon a ftrong Axis. ' 

So. The 



120 



A Courfe of Experimental Philofiphy. 



Led. III. ■ 80. The firft fort of Crane is reprefented by the 1 ft Fig. of 
Wate 12. feen in Profil. L B E D is a Seftion of that Part of a 

f-S i Z ' whai 'f e on which it is fix'd, LB being the horizontal Line. 

A C is a ftrong horizontal Piece of Timber making the upper 
Part of the Crane, into which are fram'd the three upright 
Pieces X, Y, Z, (of which, the laft call'd "the main Piece, is ftron- 
ger than the others) with its Cill I E, and its Braces H I and 
h E longer and ftronger than the Braces and Cills MN and D S 
of the other two upright Pieces, and pinn'd with Iron where the 
others are only pinn'd with Wood. When the Wharfe is not of 
Stone-work where the Crane is fix'd (as is here reprefented) 
the three Cills mull be all in one Piece reaching from D to E. 
Four Braces, fuch as K, join the upright to the horizontal Pieces. 
To the abovemention'd horizontal Piece is faften'd with ftrong 
Iron Pins, a fhort Piece// having a Bell-metal Collar to re- 
ceive the Iron Pevet or Axis of the upright Shaft R F which is 
an Axis in Teritrochio, whofe lower End of the Axis is alfo of 
Iron, turning in another Bell-metal Collar let into the firm Piece 
of Wood F. The Axis in Teritrochio, inftead of a Wheel, has 
four Bars e; /, d, and another behind V, going thro' its thicker 
Part, which is eight fquare, the upper Part being round to re- 
ceive the Rope. When this Piece is hoop'd with Iron above and 
below d, it is beft to ufe but two Bars inftead of four, pufh- 
ing them quite thro' as e b 3 and Men at each end of them go 
round in the Direction b O e to wind up the Rope and raife 
the Weight at the End of it. This upright woode;niAxl% with 
its Bars, is call'd the Capftane of. the Crane (every fucl^ Axle 
being call'd a Capftane when k turns in a perpendicular ■Situation, 
like that of the Capftanes in Ships, and a Wsndleis when it runs 
in an horizontal Pofition, tho' it lhould be for the fame Purpo- 
fes as the other) and the Rope RVrr, which goes firft over the 
Pulley or Roller T, then between the Pulleys P and and laft- 
ly over the Pulley r has at its Ends a double Iron-hook, call'd a 
Ram's-head, to which the Goods to be cran'd up are faften'd. 
The Gibbet G V B is moveable upon its Axis C B, by means 
of the Iron Center-pins or Pevets at its Ends B and C, lb that 
when the Weight is rais'd up fufficiently high, by a fmall Rope 
faften'd to it, or to the End of the Gibbet at g, it may be ea li- 
ly brought from over the' Ship , or Barge, fuppofed on the Wa- 
ter at W, to a Cart, or any other Carriage on the Wharfe to- 
wards 




121 

wards won the right or left of the Piece Z. There is a Roof Left. HL 
or fmall wooden Shed A a Q to fhelter the Rope from Rain, v^yvj' 
when the Crane is not in ufe, the Gibbet being brought under it 
towards Y. 

The fecondFigure * fhews the Plane of the upper Part of the* Plate 12. 
Crane, or as it would be feen from above, where we are to ob- F 'g *• 
ferve the Pofition of the Pulleys P and Q^, and of the Place of 
the Center of the Gibbet which muft be at C, in a Line touch- 
ing the Circumference of 'both the Pulleys ; for if the faid Cen- 
ter of Motion of the Gibbet were in a Line with the Center 
of the Pulleys, the Gibbet when, loaded would require a Force 
to bring its End g over the Wharfe on either Side, and that Force 
ceafing to a£t, the Weight and Gibbet would run back and reft 
over W. See this more particularly explain'd in the Notes, 
where the 3d Figure, being Part of the Crane and various Situ- Ann n 
ations of the Gibbet and Rope drawn by a larger Scale, is confi- 
der'd . *pi ate la> 

This Crane is very expeditious with many Hands, it being Fi S- 3- 
always requifite that fome fliould ftand at the Bars to keep the 
Weight from running down again, which might be of dange- 
rous Confequence. . But if inftead of the Capftane at O, there 
was an Iron endlefs Screw, and horizontal Wheel and Axle (com- 
monly callM a Worm and Wheel) fix'd to the Piece X made 
very ftrong for that Purpofe, or a Machine in the manner of 
Fig. ii,. of T late 11. only with a Pinion inftead of a Screw at* pi i r 
GH, making the Axis EF fhort and the Axis M long to re.Ffg.'i 3 .* 
ceive the Rope ; then two Men, nay fometimes one Man, may 
eafily draw up Goods from a Barge; becaufe by the Refiftance 
of the Screw againft the Teeth of the Wheel the Machine will 
hold the Weight at any Height, whilft the Man quits the Han- 
die to bring the Weight by the Guide-rope faften'd at g *over a* P i ate 
Cart on the Wharfe to receive it ; and yet the Weight will goFig. 1 " r 
down gently of it felf, if a Man with a fudden Jerk fets the Han- 
dles a going the contrary way to that whereby he rais'd the 
Weight which is convenient for loading the Cart. N. B. This 
fudden Impilfe on the Handles does to the Screw what a Blow 
does to the Wedge to fet it a going * . As this laft fort of Crane* No s7 
with a Worm and Wheel does very much encreafe the Force 
of the Power, I need not put the Reader in mind that more 
Time muft be fpent in raifing the Weight; becaufe the Velo- 
city of the Weight, compar'd with that of the Man's Hand who 

& turns 



l,e£h III. turns the Handle, muft be diminifh'd in a i-eciprckal Proportion? 
-s^-v-n, of the Intenfity of the Weight to the Intenfity of the Man's 
*L. 2. 9. Force *. This being true in all compound as well as fimple: 
,a - * 7 * Engines. 

* Plate ix. 81. The fourth Figure * reprefents the Rat } s-tail Grain j not 
Fi S- 4- only ufeful on a Wharfe to crane up heavy Goods, but al- 

fo of great Service in Building to raife great Stones and bring; 
them round to any defign'd Place. It confifts of the fol- 
lowing Parts. On the Grofs-ground Cills L L L L L L is fup- 
ported and fix'd by oblique Braces the ftrong upright Piece K 
Call'd the Gudgeon of the Crane, on whofe upper Part or Spin- 
dle S cover'd with Iron (and fometimes made wholly of I ton)? 
the whole Machine turns, being eafily mov'd from C to G, 
when it is charged with its Load H. C A is the Counter-wheel 
with its Axis DB bearing only on the Iron Ends of the faid 
Axis in two hanging perpendicular Pieces at B and /F is the 
Brace and Ladder, whofe Top F carries the Pulley above the 
Weight, the other Pulleys being in the Ends of the Pieces M, N, E 
the remaining Parts are too plain in the Figure to need farther 
Explanation. The Power is fometimes applied by means of a. 
Rope on the outer Circumference of the Wheel A, but moil 
commonly Men,, or an Horfe, ©r an Afs, turn the Wheel rounds 
fey walking in it. Sometimes alfo Strength is gain'd by having;, 
the Counter-Wheel made with Teeth, and giving Motion to its 
Circumference by Means of a Pinion.. 

* Plate ». .82. The 5th Figure * reprefents a Jack, which is an Inftru* 
ffig. j» ment of common Ufe, for raifing heavy Timber or very great 

Weights of any land ; but as the Wheel-work of it is {hut up 
in the ftrong Piece of Timber C B,. I thought it not impro- 
Plate s*.per to reprefent the Infide of it in Fig. 6. * where you muft only, 
fig,.«. iUppofe the Rack A B at leaft four times as long in Proportion. 

to the Wheel Q. (the f igure of the Rack being here contracted? 
for want of Room) and the Teeth, which will then be four 
times more in Number, to be contain'd about three in an Inch.. 
Then if the Handle be feven Inches long, five Turns of it, that 
is five times 2 2 Inches, ©r 110 Inches will be the Velocity of the 
Power, whilft the Weight rais'd by the Claw A, or deprefs'd 
by the Claw B moves one Inch ; for as the Pinion has but four 
iieavesj, and the Wheel Q. twenty Teeth,, there muft be five Re- 
volutions 



j4 123 



Solutions of the ^Handle fixM to it to turri the (aid Wheel once JU£t v III* 
round, whofe three-leavM Pinion R. will ia that Revolution juft VVW 
move the Rack three Teeth, or one Inch, This might have 
been alio known without feeing, or even knowing the Numf 
bers of the Teeth of the Wheel and Pinions, by meafuring a Re- 
volution of the Handle in Fi^. 5. and comparing the Space gone 
thro' by it with the /Space gone thro' by the End A or B. So 
in any other compound Engine, we may judge of its Force by 
comparing the Velocity of the Part to which the Power is ap- 
plied with the Velocity that moves the Weight, as has been 
before fliewn *♦ Sometimes this Machine is open behind from* 3** 47* 
the Bottom almoft up to the Wheel to let the lower Claw 
(which in that Cafe is turn'd up as at B ) draw up any Weight, 
When the Weight is drawn or pul^'d fuffidentt^ it is kept 
from going back by hanging the End of the Hook S fixM to a Plate 
Staple over the curv'd Part of the Handle at b. All the Work Fig. 5« 
muft be made very ftrong in this Machine, but chiefly thofe 
Parts which, immediately fuftain the Weight ; and this muft alio 
be obferv'd in all other compound Engines. 

83. All the Mechanical Powers are united together in the 
Machine reprefented by the firft Figure of Tlate 13 *, which Plate 15. 
refembles our common Chimney Jacks for roafting Meat. In a Fi §- *\ 
Frame A B C D faften'd by the Nut 0 upon the Stand 0 0, and 
held together by the Pillars V W and .B-.-#, is adapted firft the 
Piece E F, whofe Fans or Flies may be put in Motion by the 
Wind, or drawn by an Hair faftenM at F, which reprefents the 
leaver and Balance : At right Angles to this Piece is joynM the 
perpendicular Spindle G H having upon it the endiefs Screw H, 
which may be alfo confider'd as a Wedge * : This endiefs Screw * <*3> 
or Worm takes the skew Teeth of the Wheel K, which is the 
Axis in TeritrochiOj and, in turning round, winds up the String 
L M upon its Axis, which paffing round the Pulleys at M and 
N (or drawing by 'a Tackle of Five) raifes the Weight P. But as 
the Screw has no progreffive Motion on its Axis, it cannot here 
be faid to take in the inclin'd Plane; therefore to make this 
Engine take in all the mechanical Organs or Powers abovemen^ 
tion'd, we may add the inclinM Plane r #Q.R by making it 
reft on the Ground at QR, and on the Pillar q B at q r, and 
thereby the Force of the Power drawing at F will be farther 
encreas'd in the Ratio of Q^T to T S*. The whole Force gainM * 49* 

R 2 by 



24 A Courje of Experimental Philofophy. 

III. by this Machine is found by comparing the Space gone thro' by 
^Jthe Point F, with the Height that the Weight is rais'd in any 
47- determinate Number of Revolutions of F *. An hundred Pounds 
Weight at P will be eafily rais'd by the Hair of a Man's Head 
drawing at F. 

84. In the Machines abovementiWd, both fimpleand com- 
pound, the Power according to its Intenfity is fo applied to- 
one Part of the Machine as immediately to a£t upon the Weight 
whofe Refiftance deftroys all the Force of the Power, when an 
^Equilibrium is made by giving the Body mov'd and the Mover 
a Velocity reciprocally proportionable to their Intenfities ; and 
when the Product of the Power into its Velocity exceeds that 
of the Weight into its Velocity, there is no more Momentum 
left to the Power, but fo much as it has more than the Weight *. 
But there are other mechanical Organs, in which the Force 
of the Power is accumulated, and, as it were, condens'd, before 
the Weight is afted upon at all; fuch as an Hammer, the 
Cock of a Firelock which carries the Flint to ftrike upon the 
Steel, the Battering-ram (already mention'd bv the by in ano- 
ther Lecture) the Rammer to drive Piles into the Ground, the 
Fly applied to Printing or making a Stamp on Medals or current 
Coin (curforily taken notice of in this Le&ure *) and the Pen- 
dulum ; and in a word, whatever is made ufe to give a fudden 
Blow, or ftrong Impreffion inftantaneoufly ; which tho' all re- 
ducible t© geometrical Calculation, whereby one may be certain 
of their Effects, yet cannot be explain'd from the Principles al- 
ready given ; and therefore the Confideration of them muft be 
defer'd till we have explain'd thofe Laws of Motion on which 
they depend. In the mean time I think it not improper to 
give Sir I faac Newton's Account of all the mechanical Powers 
by one Scheme, as he has explain'd them in the fecond Corol- 
lary to his Laws of Motion;, for tho' that Explanation depends 
upon fuch Laws as are to be hereafter con fider'd, fo much of 
them as is contain'd in his firft' Corollary being taken for gran- 
ted, will ferve our prefent Purpofe*- 

85. If upon a Body * at A two Forces a il at onc&j, whofe 
Intfnjities are as the Length of the Lines A B and, A C, and 
DireBions in thofe Lines ; the Body fo acted upon will defer ibe 
®hs. Line A- D. the. Diagonal of the Parallelogram compleated by 



M Cdwrfc of ExperifneM PhiJo/bphy. r 2 5 

drawing the two Lanes C D and D B reflectively equal £0^Le£h" 
parallel to the two former i and that "Diagonal will he defcriPd %sy°\J 
by the joint Forces in the fame Time that either of the Forces. 
Jmgly would have caus r d the Body to go thro* the ' Line AB or 
A C. And as by Comgojition of Forces a Body will move in the 
Line AD ; fo like wife a Body moving in the Line A D, tho r 
by the AStion of one Jingle Force j may be conjider y d as if it had 
been a£fed upon by two Forces ^ namely^ rejblving the Jingle Force 
into two j as A Q and A B* 

86. If the- unequal/ iW/i' O M *" arid ON drawn" Frpm the*. Plate2S . 
Center O of any Wheel fhoulcl fuftain the Weights A and P by Fig. V- ' * 
the Cords M A and N P ; and we wouM know the Forces of 
thofe Weights to move the Wheel. Through the Center O draw the 
right Line KO L, meeting the Cords perpendicularly in K and 
L; and from the Center O with Q L? the greater of the Di- 
fiances O K and O L, defcribe a Circle, meeting the Cord M A 
in D : and drawing O D, make A C parallel and D C perpen- 
dicular thereto. Now, it being indifferent whether the Points* 
K, L, D, of the Cords be fixM to the Plane of the Wheel or 
not, the Weight will have the fame Effe£t whether they are 
fufpended from the Points K arid L, or from D and L. Let 
the whole Force of the Weight A be reprefented by the Line 
AD, and let it be refolv'd into the Forces AC and CD; of 
which the Force A C, drawing the Radius O D dire£Hy from 
the Center, will have no EffeS: to move the Wheel : But the 
other Force D C, drawing the Radius D O perpendicularly, will 
have the fame Effect as if it drew perpendicularly the Radius 
0L equal to OD; that is, it will have the fame Effe<£fc as the 
Weight P, if that Weight is to the Weight A as the Force D C 
h to the Force D A ; that is (becaufe of the fimilar Triangles 
ADC, DO K) as OK to OD or O L Therefore the Weights* 
A and P, which are reciprocally as the Radii O K and O L thafe 
lie in the fame right Line will be equipollent, and fo remain 
in MquilibriO) which is the well known Property of the Ba? 
lance, the Leaver and die Wheel. If either Weight is greater 
than in this Ratio, its Force to move the Wheel will .be w fb- 
much the greater- If the Weight equal to the Weight P, is> 
partly fufpended by the Cord Np partly fuftained by the ob- 
lique Plane p G ; draw ^ H, N H, the former perpendicular tor 
the Horizon, the latter to the Plane $ G ; and if the. Force of 

- the.: 



Left. III. the Weight / tending downwards is reprefented by the Line/ 
K^TSj it may be refolv'd into the Forces p N, H N. If there was any 
Kane perpendicular to the Cord / N, cutting the other Plane / G 
in a Line parallel to the Horizon ; and the Weight/ was fupport- 
ed only by thofe Planes / Q*/G; it would prefs, thofe Planes per- 
pendicularly with the Forces / N, H N ; to wit, the Plane/ Q with 
the Force / N r and the Plane / G with the Force H N. And 
therefore if the Plane p Q/ was taken away, fo that the Weighe 
might flxetch the Cord, becaufe the Cord now fuftaining the 
Weight, fupplies the Place of the Plane that was remov'd, the 
Force pf that Weight will be obtainM by confidering it as the feme 
Force / N which prefs'd upon the Plane before. Therefore the 
Tenfion of this oblique Cord / N will be to that of the other per- 
pendicular Cord / H as / N to p H. And therefore if the Weight 
/ is to the Weight A in a Ratio compounded of tlxe reciprocal Ra- 
tio of the leaft Diftances of the Cords / N, A M, from the Center 
of % he W heel, a nd of the dire£t Ratio of/ H to / -N ; the Weights 
Wit) have the feme Effefl: towards moving the: Wheels and will 
therefore fuftaln each other, as any one may find by Experiment. 
. But the Weight / preffing upon thofe two oblique Planes* 
may be confider'd as a Wedge between the two internal 
Surfaces of a Body fplit by it ; and hence the Forces of the 
Wedge and the Mallet may be ^determined \ for becaufe the 
Force with which the Weight ^ prefles the Plane / Q, is 
to the Force with which the fame, whether by its own Gra- 
vity , or by the Blow of a- Mallet , , is ; . impelled in the Di- 
rection of the Line / H towai^ds both the Planes, as / N 
to /H; and to the Force with which it preiles the ather 
Plane / G, as / N to N H. And thus the Force of the Screw 
may be deduced from the like Refolution of Forces ; it be- 
ing no other than a Wedge impelled by the Force of a 
Leaver. Therefore the Ufe of this Corollary fpreads far and 
wide, and by that diffufive Extent the Truth is farther con- 
firmed... For on what has been laid depends the whole Doc- 
trine of Mechanics , varioufly demonftrated by Authors. For 
from hence are ea.fily deduced the Forces of Machines, which 
are compounded of Wheels, Pulleys, Leavers, Cords and Weights 
afcending dire&ly or obliquely, and other mechanical Powers ; 
as alfo the Force of the Tendons to move the Bones of A- 
nimals. 

End of the Third; Lecture, 

Anno- 



127 




4TI0NS wpon tm Inird JmEcture. 






I* C i • • Simple Machines ^ or Organs, < calTd byfime Mechanical Faculties^ 

or Mechanical Powers.] 

PHE Word Power here is to be taken in a very different Senfe- Annotate/ 
from what it bears in the Second Lefture, where the Word Left. III. 
Power * (jfignifying whatfoever is made ule of to raife a Weight) s^v-^° 
is defined at large.} for here it only lignifies the Organ or Inftrument * L. a.. No. 
whereby a Power of known Intenfity is made to aft upon a Weight s 1 ^ 
and therefore we muft take care not to attribute any real Force to any 
iimple or compound Machine^ as a great many People are apt to do mere- 
ly becaufe the Name has been given : to Mechanical Organs, not 
from their Effeft, but from the Effect which the Power produces by their 
Means } for how much fbever the Forpe of a Power is thereby encreafed 
in order to luftain or raife a Weight far. fiiperior to it in Intenfity 5 yet 
this cannot be done without lofing in Space and Time what is gain'd in 
Force, contrary to what fome have vainly imagined, becaufe the Vulgar 
commonly lpeak of a Machine as they do of an Animal, and attribute 
that Effeft to the Machine, which is the Effe£t of the Power by means 
of the Machine, as it is ufual to lay, Such a Machine raife ^s fuch 1 a Quan- 
tity of Water, or ' performs, fuch and fuch Work y . when we Ihould fay, if 
we would lpeak in > the proper and PhilofophicalSenfe, a running Stream,,, 
fuch a Fall of 1 Water, the Wind, or fo many Men, Horfes Sec. raife 
fo much Water in fuch atfime, &c. by fuch or fuch a Machine^ as we have 
obferv'd in the: Notes on the laft , Le&ure It were therefore to be* A 
wilh'd, that the Word Power were confin'd to its proper Senfe, and not L 2 nn ' 
ns'd to fignify a Mechanical Organ ^ but as it has been cuftomary to ufe it ' 
in that Senfe, I thought proper alio to, make ufe of it j , but withal to give : 
this Caution* 

2. C?. reducing all the Mechanical Powers to the Leaver, or explains 

ing all their Operations by that of, &c.J Tho' one may eafily fhew (as we: 
fliail at the End of this Note) that every other Mechanical Organ does 
potentially contain a Leaver ^ that is, that if fo much of every other fim«, 
pie Engine was cut away as to leave, only a Leaver, the fame reciprocals 

Proppr- 



'Annotat, Proportion between the Velocities of the Power and Weight and their 
Le£L III. Intenfities - 0 would as plainly appear on ftch a Leaver as on the Engine^ 
w^/~s^ before it is reduced to it: Yet we are not from thence to conclude, that the 
'Leaver alone might be made to ferve for the Purpofes of all other Me- 
chanical Organs for they are contriv'd of different Forms to anfwer to 
different Ways of working, requir'd in Mechanical Operations for the 
Ufes of Life, it being lometimes impoffible to life one Mechanical Organ 
inftead of another ^ and always more convenient to apply one than another^ 
the Choice of which depends upon the Skill of the Artift.x 

Thus in the Balance (whether a Pair of Scales or a Steel-yard) the 
Commodity to be bought, or heavy Body whole Quantity of Matter is to 
be eftimated, is not to be rais'd with any Velocity, but only luppofed to 
make an JEquiUbruim with a known Weight, which in this Machine ferves 
for a Power : B,ut a Weight is leldom or never made ufe of as a Power in 
any other Mechanical Organs, except, in fome few, and thole Engines 
which the Ancients made ufe of in War, which are now out of Ufe. 

The Force of one or more Men is the Power applied to the- Leaver j 'there 
the Power muft always overcome the Weight, by adding a little more Ve- 
locity or a little more Intenfity to the Power, over and above the reci- 
procal Proportion requir'd in the Balance. - With this Inftrument heavy 
Bodies are removed a little way at a time, as great Stories in Buildiftg, 
large wooden, leaden, or iron Pipes in Water-works, and large Pieces of 
Timber } but Leavers will; only ferve to raife thole Bodies high enough to 
lay them on a Carriage, &c: 

But if we wotfd raife up a Stone to a confiderable Height to lay it in 
its proper Place in a Building, or any other Body to any Height above 
three or four Foot, the Leaver becomes ineffe&ual, and then we muft ufe 
* 97, 5^^ 39- Pulleys in fome of the Ways mentioned in this Lefture Tackles of Pul- 
*°>4 l « leys are very convenient where there is no room for aCapftane, and where 
Bodies are to be rais'd in different Places, becaufe they are eafily moveable ; 
but the Weight muft not be too great, by reafbn that many Men cannot 
pull at once, and equally, by one running Rope } and if the Power was 
to be very much encreasM by the Number of Sheevers or Wheels in the 
Pulleys or Tackles, the Rope muft be of a' prodigious, and therefore incon- 
venient, Length. 

An Axis in PeritrochtOj Capftane or Windlefs, which are all the lame 
Organ differently pofited, is of ufe where Pulleys are deficient. For Ex- 
ample, if Water is to be drawn out of a deep Well, a Wheel with Arms 
or Spokes ferves to turn the Axle on which the Rope winds to bring up 
the Bucket or Buckets In Building, a Capftane whofe Make gives the 
Power no more Advantage than a Tackje or Pulley of many Sheevers, is 
yet more uleful, becaufe it will admit of eight, ten, or twelve Men to worjc 
-at it and pufli its Bars, when only three or four could pull at the running 
Rope of the Pulley. If the four Bars of the Capftane are fo long that 
three Men applying their Strength to each of them, the Man in the 
middle of the Three is at the Diftance of three Foot from the Axis of 

Motion, 



ACourfe of Experimental Pbikfophy. 129 

Motion, and the Axle on which the Rope winds is of fix Inches Diame- Annotate 
ter, thofe twelve Men will do the Work of 72, but in the fixth Part of Lett. Ill 
the Time. The lame would be done, and in the fame Time, by two Men t/YV° 
walking within a vertical Wheel of 24 Foot in Diameter (fuch as is call'd 
by fome a Counter Wheel) whofe horizontal Axle might be of eight In- 
ches Diameter ; and about the Weight of one Ton and an half, or two 
Tons, might thus be rais'd by either of thefe Machines. But if at a 
Wharfe, where only two Men ihould be employed to work at the Crane, 
it was required to draw up heavy Blocks of Marble of three or four times 
the Weight abovemention'd (for a Block of Marble fix Foot lpng^ four 
Foot wide and four Foot deep will weigh between 7 and 8 Ton) the Counter- 
wheel muft be 72 Foot in Diameter for an Axle of eight Inches, which 
is impracticable, on account of the Bulk and Coft^ or the Axle muft be 
made three times lefs in Diameter, and then it cannot be ftrong enough to 
bear the Weight. In fuch a Cafe therefore there muft be a compound 
Axis in Peritrochio, fuch as is defcrib'd in this Le£ture # , but with one* No. 47. 
more Pinion \ for example, if an Iron Wheel with Teeth of four Foot in 
Diameter be fix'd to the abovemention'd Axis of eight Inches Diameter, 
and that Wheel be lead by an Iron Pinion of fix Inches Diameter, whole 
Wheel is of three Foot Diameter and lead by a Pinion of eight Inches Di- 
ameter, whofe Handles are a Foot long, the fame Operation will be per- 
formed by two Men, but they muft employ three times more Time. 
N. B. If the Teeth of the Wheel be of Erafs, and the "Teeth or Leaves ef the 
Pinions of Iron *, the Machine will move more fmoothly, and the "Teeth wear 
equally. 

The Numbers of Teeth in the Wheels and Pinions may be as follow 

The firjl Pinion, to which the Handles are fi^d^ 28. 
The fir ft Wheel, led by the faid Pinion^ 112. 
The fecond Pinion , 19. 
The fecond Wheel, 171. 

Jnd the Axis on which the Rope winds muft be of about eight Inches r 
becaufe it immediately bears the Weight by the Rope, which runs 
over fome upper Pulleys or Rollers that add no Force to the Power. 

If the Capftane with Bars abovemention'd, be fix'd to do the Work for 
which it is proper, and unexpeftedly there fliould be occafion to lift very 
heavy Weights, there is no Neceffity for taking it down to fet up fuch 
a Combination of Wheel-work as we have juft defcrib'd, becaufe a Pair of 
Blocks to help at fuch a Time may be fix'd in any Part of the Building 
over the Place where the Weight is to come up and receive the Rope from 
the Capftane, fo as to encreafe the Force of the Power, according as the 
Blocks are a Tackle of Two, of Three, of Four, or Five, Sec. and then the 
Blocks may be taken off again, and the Capftane work'd as before. In 
the Ufe of the Counter-wheel or RatVTail Crain * the Power may be al- * No. 8z. 
fo thus occafionally encreas'd. 

S Where 



1 30 A Courfe of Experimental Philofophy. 

Annotat. Where there is no Room for the compound Axis in Peritrochio of two 
Le£t. III. -large Wheels and Pinions, the fame : may be affected by making a Worm- 
%S*tf°sj fcrew of one Thread turn'd by two Handles of a Foot long, each, tO/lead 
a Whfcel of two Foot Diameter, having 72 Skew-Teeth, and a Wooden 
, Barrel or Axle of 8 Inches Diameter, the Advantage of which Machine is 
*No.7g,Si..ihewn in this Lefture *. 

If Hogfheads or Pipes of Wine, or other Liquors, are to be let down, 
into a Cellar, or brought up out of it* a Plank is laid along the Stairs^ 
which in that Cafe is an inclined Plane , the only mechanical Organ fit for 
that Purpofe : So likewiie in making Refervoirs for Water, in gardenings 
and in building Fortifications, where Carts can't come, inclined Planes made 
©f Wood ferve effectually for Wheel- barrows to run on in removing the 
Earth from a lower to an higher Place. 

In cleaving Wood, the Wedge only is of Ufe \ for an Hatchet, which, 
snay cleave fmall Wood, is only a Wedge with an Handle. Another con- 
fiderableUfe of a Wedge, is the railing up a Beam to underprop it when & 
Floo£ begins to give Way, by reafon of too great a Burthen laid upon it,... 
as in a Ware-houle$ and fo much Force may be applied this Way, that 
ibme thouifand Tons may be rais'd up together with the Floor, and ail 
lecur'd by means of this fmall Machine. For tho' Screws turn'd by long 
Leavers might ferve in a great meafure for the fame Purpofe, there muft 
be Space to go round with the Hand-Spikes, which cannot be had when 
the lower Part of the Ware-houfe is full of Goods, without removing, 
them with great Trouble and Coft. See the Manner of performing this 
in the 4th Figure of Plate 13. 
llkte 1 J* B A b D E C is a Beam, which in the horizontal Situation* iharic'd by, 
Big. 4. the prick'd Lines Bh and CD fupports a Floor. Now when very great 
Weights being laid upon the laid Floor, make it give way and bend into the: 
CurveB A£, or, which is the fame, C E an upright Poft V p is fram'd 
into a flout Plank F F, and an horizontal Piece E (here feen End- wife) is 
fiip'd under the Beam, and on the Top of the Poft} then the two Wooden, 
Wedges W, w> as broad as the Poft, are driven in with heavy Hammers^ 
in ftriking at once in contrary Direffions, fo as to let the Beam ftreight^ 
and reduce the Floor to its Place, without removing any of the Goods that 
lie on the laid Floor,, or moving any of thole below, but juft to make 
Room for the Poft and Plank. 

The Ufes of the Screw for railing, finking, drawings pulhing, preffing^ 
or joining together Bodies, are commonly known ; and it is evident by In* 
fpeO:ion 5 that no other of the mechanical Organs will anfwer the fame Pur- 
f ofes> 

" Now tie mll.JfcemhoM. all the., mechanical Organs or Inftmmentsmayhe re- 
du^d to the Leader.. 

This has been already ihewn concerning the Roman Balance (and is ap- 
plicable to the common Pair of Scales) by the 6th Experiment of this 

El. 9, F, 11. 

Secondly^ 



A Courfi of Experimental Thilofophy. x*r 



Secondly., Pulleys are thus reduced to the Leaver *, An upper Pulley as Annotat% 
ED {Plate io- Fig. 3.) appears plainly to be a Leaver of the firft : Kind, Left. III. 
by cutting away ail the Sheever, except the prick'd Line E D, which about i/vv 
the Center C keeps in Mquilibrio two equal Weights. In the 4th Figure\*? lM I0 - 
the lower Pulley ge, by leaving only the prick'd Line ge 9 . and Center Pi« + fijlte 10, 

appears to be a Leaver of the fecond Kind, whereby a Power applied at pi g . 4 , 
g 7 does in the Direction gd raile a Weight W fufpended at the Center Pin 
It is laere evident, that e is the fix'd Point or Fulcrum of the Lea- 
ver, ge the Pittance of the Power, and ce the Diftance of the Weighty 
and accordingly, in the Experiment, the Power P : is to the Weight W ; ; 
as c e: to g e H 1 : 2* And by comparing the compounded Leavers of 
Plate 9. Fig. 14. with the Syftem of Pulleys of Plate 10. Fig. 9. one ma yp| ^ F t 
fee that the four Pulleys reducM to their horizontal Diameters, a& upon " 
one another as four Leavers of the fecond Kind, in every one of which the 
Diftance of the Power is Two, and that of the Weight is One, and there* 
fore the Ratio compounded of them all # , is that of the Weight to the* j^ Q# 
Power, or 16 to 1 ; for 2%2%i%i^i6. Or comparing this Syftem of 
lower Pulleys with Fig. 5. of Plate 15 , which is juft fuch a Syftem or Aflem- 
blage of Leavers of the fecond Kind, where the Leavers are imrk'd with 
the fame Letters, as well as the Forces pulling down each Leaver *. *pj ^ p 5 

One may, by the nth Figure of Plate 10, eafily reduce an Axis in Pe- 
ritrochio to a Leaver of the firft Kind, repreien ted by the prick'd Line 
E T, the fix'd Point being at K, the Power being applied at E, and dif- 
ferent Weights fucceffively at the Points A, B, and T, cutting away the 
reft of the Machine. But as the Rope fuftaining the Weight does not 
move in the fame Plane as the Rope drawn by the Power, it is better to 
confider it as a Leaver of the firft ICind twice bended, and an Axis Df 
Motion going thro' one of the bended Parts, as in the 6th Figure*, where* pkte ij. 
the bended Leaver AC ^B moves on the Axis II fix'd in the Frame Fig. 6. 
I K L I. Be reprefents the Radius of the Axle, and AC the Radius of 
the Wheel, fuppofing B c and A C in the fame Plane, and at right Angles 
to the Axis ; otherwife, if oblique, they muft be redue'd to right ones, by 
calling their Lengths only the perpendicular Diftances of B and A from the 
Axis II: Then P being the Power, and W the Weight, the reciprocal 
Proportion will be thus, AC: Br;;W : P. 

To reduce the inclin'd Plane to a Leaver, we muft look for a bended 
Leaver in the Weight rolling up the Plane, whofe Arms fhall be as the 
Length of the Plane to its Height. 

Since the Triangle A B C * is fimilar to w Y B (by 4. 6. EucL) and*pj a te9* 
wYB fimilar to wBN (by 8. <5.) in the bended Leaver ^BN, wB:Fig. 14. 
BN AB : BC Now, fince is the Line of Direction of the Weight 
w 7 that Weight may be confider'd as preffing on N B the fliort Arm of 
the Leaver at the Point N, the Center of Motion being at B, where the 
Ipherical Weight touches the Plane, and the. Power applied at right An- 
gles at the End wo£ ?vB the longer Arm of the Leaver , therefore, calling 
P the Power, and w the Weight, P : w ; : N B : B w ; ; AB ; B C. 

S 2 N/B. 



i g2 A Courje of Experimental Philofophy. 

Annotac. N. B. Here the Power by a Rope over the Pulley M, draws in a DireUion 
Left. III. parallel to the Plane; but if it drew in any other Direclion, one might 
C/'VNJ calculate the oblique Force of the Power by means of a bended Leaver. 

But we mufl refer this to our particular Obfervation of the inclined 
Plane, and ftatical Confederations, in other Notes ; except the Direblion 
parallel to the Bafe, which reduces the Wedge to a Leaver. 
Now the Triangle ABC mufl; reprefent the Wedge, which being driven 
under the Weight, makes it rife up the perpendicular Height C B, while 
the Power drives the Wedge the Length of its Bafe AC, or, which is the 
fame Thing, the Power n draws in the Line wr parallel to the Bafe AC. 
Here the bended Leaver is OBN, with the ihort Arm N B fupporting 
the Weight at N, while the Power faften'd to O draws the Arm OB at 
right Angles. 

Authors have fliewn other Ways of reducing the Wedge to a Leaver : 

* Plate 13. F or example, the Wedge B F C * of Plate i ? . Fig. 7. is confider'd as a 
»• Leaver of the lecond Kind, whofe Fulcrum is at F, and the Weight at 

W ; which moving round the Center of Motion F, by a Power carried on 
at the End of the Leaver from A to L, raifes up the Weight W. Or 
elfe, the Leaver being kept by the Prop B, fo as always to make the 
fame Angle with the Horizon, is carried on from the Pofition CF B into 
the Pofition cfb„ the Fulcrum advancing forwards along with it to raife 
-* Plate 15. the Weight to w. In the 8th Figure *, where two Bodies are feparated to 
*'& 8 - reprefent the cleaving of Wood, the Wedge is reduc'd to two Leavers 
of the firft Kind, having the Fulcra at F, /, the Weights at W, w, and 

* Plate 13. the Powers at L, /. Or in the 9th Figure*, two Leavers of the fecond 
'•S- 9- Kind are fuppofed to be very thin, and thruftin between the two Weights, 

fo as to prefs againft each other's Ends, and make a common Fulcrum at 
F, the Powers moving from L,/, to a and b, while the Weights W, w 
are feparated: Or elfe (what comes to the fame Thing) the faid two Lea- 

* Plate 13. vers being join'd in a fix'd Angle by the Prop L / {Fig. 10.*) are confider'd 
fr'g- I0 - as thrufl: in between the Weights, while the common Fulcrum advances 

in the Line FG. But becaufe in all thefe Ways of explaining, the Dif- 
tance of the Power (and confequently its Force) is continually changing 
which is not true in the Wedge; I would rather propofe another Method* 
which will agree with the Cafe of the fingle Wedge or double Wedge (dif- 
*No.55,5<5.tinguilh'd thus, as the Inftrument a£ls with one or both Surfaces*) always 
making the Diftance of the Power and Weight to keep the Proportion 
agreeable to the Angle of the Wedge. As for example, in the Wedse 
o piate 13. L F W Fig. 11.* L F W is a bended Leaver, whofe ihort Brachium 
Fig. 11. always remaining the fams, lifts up the Weight «, and brings it tow 
whilit the Leaver turns round the Center F, the Power at L defcribing the' 
Arc hi: So in the double Wedge Fig. 12. two bended Leavers, moving 
round the Center F, by their Ihort Arms F W, F w, feparate the Weights 
W,w j and when they have brought them round to X and *, the long 
Arms L F, / F turning round F in the Arcs L M, / M, one may fee that 

the 



A Courfe of Experimental Philofophy. rgg- 

the fame Thing is performed as if the whole Wedge FM had been driven Annotat. 
between them in the Direction NM. Left. IIL 

Having fhewn that the Screw afts either as an inclined Plane, or as a 
Wedge, it is evident that what has juft been faid reduces it to a Leaver. 

^ % j- — , — ^he Quantity of FriSlion in Engines will he confided d y That 
there is a Lofs of Force in the working of Engines on account of the 
Rubbing or Fri&ion of their Parts, has been obferv'd by moft Writers of 
Mechanics; but that Fri&ion has not been enough confider'd by them : 
Upon which Account, feveral Perfbns (who having applied themfelves to the 
Study of Mechanics are not yet much acquainted with the Pra&ice) imagine 
By comparing the Effects which are performed by means of fuch Engines as 
they examine with the Powers apply'd to them, that the Machine muft be ve- 
ry ill contrived, becaufe the Effefl: does fo much differ from the Calcula- 
tion which they make exclufive of Fri&ion fuppofing indeed that lome- 
thihg is to be allow'd on that Account^ but nothing near what they find 
to be loft in Force, PolTefs'd with this Notion, Projectors contrive new 
Machines (new to them, tho' perhaps defcrib'd in old Books, formerly 
praftis'd and then difus'd -and forgot) which they luppofe will perform 
much more than they have feen done with the fame Power 3 becaufe they 
allow too little for Friffion. Full of this they go to the Charge of 70 or 
80 1 for a Patent for their new Invention then divide it into Shares and 
draw in Perfbns more ignorant than themfelves to contribute towards this 
(fuppos'd advantageous) Undertaking till, after a great deal of Time 
and Money wafted, they find their own Engine worfe than others which 
they hoped by many degrees to excel. This has been very much the 
Pra&ice for thele laft twenty Years : For tho' fome Projectors have .been 
altogether Knaves - 0 yet the greateft part have firft deceiv'd themfelves 5 
and thole who are really deceiv'd, by their Eagernefs and Earneftncfs moft 
eafily deceive and draw in others. For this reafon, I thought it would be of 
Ufe to the Publick to give as full an Account of Friction, as I poffibiy 
could gather from the Experiments made by others (elpecially the Members 
of the Royal Academy at Paris) and my own Experiments and Obferva- 
tions. 

We fliall not here confider, that Friction or rather Refiftance which a- 
rifes from an ill Contrivance of the Parts of an Engine which are to ad 
upon one another by Application - 0 making thole Parts a£t obliquely which 
ought to aft at right Angles, or at leaft more obliquely than they fhould 
do:, that being owing to an incomplete Theory or a bad Workman. But 
jonly that Fri&ion, which is unavoidable from the Nature of the Materials^ 
however polifhM, at the firft ] making ufe "of an Engine /, and that which 
Time brings on, as the Parts wear unequally, or grow nifty or rotten for want 
of Oil,. Greafe, or by conftant Ufe: So that the touching Surfaces, which 
were as fmooth as the Hand of a skilful . Workman could make them, be- 
come very rough and uneven by this means, and add much Fri£tIon to that 
which, on account of the Nature of the. Materials, could not be avoidfed 

at 



i 34. A Courfe of Experimental Philopphy. 

Annotat at firft. So an old Jack for roafting Meat requires more Weight to make 
Lecl ill. it go when the Pivots and their Holes are pretty much worn and a well 
WYV made Lock grown rufty for want of Oil to guard it from the AtWon of 
the acid Salts in the Air will not without difficulty be open'd with a rufty 
Key i tho' the Figure both of the Lock and Key be as perfeft as at firft. 
Wood will grow rotten, and iwell beyond, or fhrink from, its firft Dimenfi- 
ons by the Weather and Cords run round Pulleys or wind about Rol- 
lers with more difficulty according as they ftiffen by wet, or any way be- 
come more twifted. 

. To proceed methodically, we will confider the unavoidable Frittion of the Jim- 
pie Machines or mechanical Organs fever ally. 

The Leaver, in relpeft to the Work done with it, is fubjeft to very lit- 
tle Friftion, moving on a fmall Surface crofting the Inftrument like a Line 
where it is applied to the Prop or Axis of Motion ; which in Theory is 
confider'd only as a Point, and calf d the Center of Motion. 

When the Balance (whole Make is neareft to that of the Leaver) has no 
more Fri&ion in proportion to its Length than the Leaver ^ yet it has a 
great deal too much for a nice Balance, as may be found by Experiencee 
Few of the Scale-makers know wherein the Nicety of a Balance confifts ^ 
but generally follow a Faftiion, or, when they would excel, endeavour to 
out-do one another in Ornaments or a fine Polifh, conlulting Beauty more 
than llfe y and thinking the Bufinefs is done if they have brought the Ba- 
lance to turn with a fmall part of a Grain. 

For the Benefit of thofe who would make, and thole who would ufe 
very exaflt Scales, I fliall here mention the Faults I have found in Scales 
efteem'd extraordinary good ones and fhew in what manner I think fuch 
Faults may be avoided j as alfb the utmoft that may be expected from a 
well made Balance. 

Mr. George Graham and I laft Summer, in order to try fbme Experiments 
with Brigadier Jrmftrong^ Surveyor of his Majefty's Ordnance, examined 
a Pair of Scales made by a very nice Workman, and kept in a Glafs Cafe 
that the Air might have no Power over them. Thefe Scales were thought 
extremely nice, becaufe they turn'd with the 256th part of a Grain 5 but 
upon Examination they appear'd to differ from that Nicety fbmetimes 3 of 
the Parts above-men tion'd, which made us imagine one Brachium longer 
than the other } but at laft we found that this Difference was owing to 
* Plate 13. t h e Situation of the Axis of Motion ; for if in the Circle AaRb* (on 
Jl g- x 3« t be lower part of which the Axis or fliarp Edge of C ought to bear at A) 
the laid Edge fhould not reft at A, but at a or the Brachium on the 
other Side of A will preponderate 3 which it did in our Trials, lb as to 
make a Difference three times greater than what turn'd the Balance in its 
true Situation. Now fince the Friction encreafes in proportion to the 
Weights bearing on the Axis of Motion (as we fliall hereafter fliew) 
this Error will encreafe in the lame manner and become confiderable, as 
heavier Bodies are weighed ^ fo that w 7 hen we think we have an Mquilu 
brium^ by only lifting up the Beam E L with the Weight hanging at its 

Ends 



A Courfe of Experimental Philofophy. 1^5 



Ends in the Scale, we ihail upon letting it down again find the Mquilibrium Annotat 
to be loft* fo difficult it is to lay the Edge, or Axis of Motion upon the Lea III 
fame Place which it had before., or to give it a true Bearing at firft over v^-vtnJ 
the lower Part of the Ring at A. There is alfo another Fault which 
Scale-makers are fometimes guilty of, which is not to make the Brachia 
nicely of a length ; and then to hide that Error, they adjuft the Balance 
by filing away fome of the Thicknefs of the longeft Part of the Beam, and 
fometimes by the Scales. Others again, by making Ornaments in a nice 
Balance weaken a (lender Beam juft under the Axis where it ought to be 
ftrongeft. 

To make a very exaa Pair of Scales the following Direftions fliouid 
be obferv'd. 

1 •.The Axis C muft be made of good Steel hardened and weH polilh'd- 
but the Edge of it muft not be fo ftiarp as to cut. 

2. The two Rings on which the Axis is to bear, fuch as A ^ B muft 
alfo be of hard Steel and well polifli'd, but the lower Part of them fliouid 
be the narrow End of an Oval, the Hole being of the Figure K. The 
Planes of thefe Rings with the Pieces that carry them (here reprelented 
by m n as broken, with the Examen 0 between them alfo broken) muft be 
exaftly parallel to one another, and one and the lame Line muft be their 
common Axis. 

N.B. If thefe Rings were made of Jgate or any harder Stone well polifh'd^ 
they would do better than Steeh 

3. The Points of Sufpenfion of the Scales, fuch as S, muft be exaftly 
equidiftant from C the Middle of the Beam, and the lower Part of the 
Hole S muft be a fharp Edge of hard and polilh'd Steel. 

4. Each Scale being fitted with its Hook and Strings muft be wejgh'd 
fingly in another Pair of Scales, obferving to weigh each of them in the 
fame Scale againft the fame Counterpoife in the other Scale, without flu- 
king the Beam to alter the Pofition of the Axis in the manner above 
mentioned. 

5. When the Beam being fufpended, does by its Exarnen (that is,, the 
Sender perpendicular Piece over the Axis) appear to have its xwo-&rachia 
exadly in Mquilibrioy^ to try whether the Points of Sufpenfion are exaaiy 
equidiftant from the Axis at A, hang on the Scales (prepar'd as before 
direaed) and if they are in Mquilibrw 7 and continue fb upon changing them 
for one another, then you may be fure that both Scales and Beam are well 
adjufted. 

6. But if by the preponderating of one Scale, the Beam appears to be 
unequally divided 5 then with a Pair of Pliers bend the Part L of the 
Hook, in order to bring S nearer to, or to remove it farther from the 
Point A, and if that alters the Mquilibrium of the Beam without the 
Scales, hang a Thread or fome fmall Weight on that End of the Beam 
which has beea made fliorter, to reftore that Mquilibrium then try with : 
the Scale, and if the Mquilibrium continues, file off fo much of the heavieft 
Mrachimn, as the Weight of the, Tfaead amounts to-.. If the Beam be.; 

made. 



jq6 A Courfe of Experiment a 




Annotat. made of Steel, after the Hook LS has been harden'd, one nuift with a 
Left. III. Blow-Pipe bring down the Temper of the Part that it may be fofc 
w^V*"^ enough to bend without breaking, 

7. The Points of Sulpenfion for the Scales, as S, mtift be in the fame 
horizontal Line as the Axis A, the Scales muft hang very freely on their 
Hooks, and the Center of Gravity of the Beam muft be a very little un- 
der A. 

8* When the Beam of a Pair of Scales weighs from three or four Oun- 
ces ta about one or two Pounds, fometimes the Points of Sulpenfion of 

* Plate 13. the Scales are lhut up within Boxes at the Ends of the Beam fuch as B \ 
Fi g- J 4- thro' which a fquare Piece as Steel C paffes, whofe upper Part in the 

middle has an Edge like the Axis of the Beam, but only with the Edge 

* Plate 13. upwards, to fuftain the Eye ee, and the Hook of the Scale. Cc* repre- 
Fig. 15. fents one of thole Pieces out of the Box, and its middle Se&ionis mark'd 
^Plate 13. whofe upper Edge fupports the E # . In order to adjuft fuch a Ba- 
Fig. 16. lance nicely (all other Things being fix'd as beforemention'd) there fliould 

be a long Hole like H h # , for the fulpending Pieces as C c, to be rnov'd 

* Plate 13. fa^fo as t0 ^ e bought nearer to, or farther from the Axis of the Balance, 
lg * I7 ' by means of a Screw Pin P-, that when they come to be exa&ly equidiftant 

from the faid Axis (which can only be known by hanging on Scales 
or VVeights exaftly equal, having due Regard to the Effeft of Pins length- 
ned or fhortried without the Box at P by fcrewing) the Pieces C may be 
fix'd, the Screw Pins filed off, and the reft of the Hole fill'd up on each fide 
the Supporting Piece C. 

N. B It is not to be expected that a large Pair of Scales Jhould be fo exaft 
as a fmall Pair - 0 becaufe the Friftion encreafes according as it is heavier : 
So that if a Balance, whofe Beam and Scales weigh fix Ounces Troy, 
be turned with r 6 of a Grain, it may be faid to be as nicely adjuft ed as 
Brigadier Armftong : } s Balance abovement ion' } d, which weighing 16 times 
lefs, turns with -jfg of a Grain. So likewife when a Balance turns \ 
with a fmall Part of a Grain, we muft not expedl it to turn as eafily 
when the Scales are loaded , for they will always become lefs nice, accord- 
ing as they encreafe in TV ?ight* 
The Pulley is liable to a great deal of Friction on account of the Stiff- 
nefs of the Ropes, the Smallnefs of the Wheels or Sheevers in Proportion 
to their Center-Pins, and their rubbing againft the Sides of the Block or 
Frame in which they move. 

Great Care Jhould be taken that Pulleys, which are to be us'd in Build- 
ing, or any where at Land, fliould receive no Wet; for by fo doing, the 
Ropes twift and thicken, lb as often to require a great Force to draw 
them thro' the Blocks in that Condition, even when no Weight is raised ; 
but when one cannot avoid wetting them, tarr'd Ropes muft be ns'd as 
at Sea. 

To prevent the Wheels rubbing too much againft the Blocks that con- 
tain them, there ought to be thin Collars of Brafs or Iron of a Diameter 
much lefs than the Wheels on the Pins on each fide of the Wheel 

To 




A Courfe of Experimental 

To leffen the Friftioii on account of large Pins when great Weights are Annotat. 
to be raw d, we ihould confiderably increafe the Diameter of the Wheels, Lett. Ill 
tho' in iome Cafes the Machine would be too cumberfome, and there- 
fore not fo eafy to be managed. But as People do-aot commonly imagine fo 
much Difference as there is between fmall and large Pulleys, provided their 
Number and Combination to be the fame ; I fhall explain that Cafe in confi- 
denng the Way of finding what the Quantity of Friffion is, and only men- 
tion here that according to Monf. Amontotfs Experiments and Calculations*,* Memoirs of 
there is fo much Friction in Pulleys on account of the Force requir'd to* heR y al J- 
bend the Ropes and overcome the Friffion of the Pins when the Wheels ^wfir Ac 
or Sheeves are fmall, That if over an upper Pulley of 3 Inches Diameter W- 
with an Inch Pin, there was a Rope of f Diameter "having 800 Pound 
Weight at each End, which Weights muft keep each other in JEquilibrio 
in this Cafe (becaufe here the Pulley only does the Office of a Roller) in 
order to make one of the Weights preponderate and overcome all the Fric- 
tions, fo as to bring the other Weight over, one muft add 4? 6 f to that 
Weight, calTd the Power in fuch a Cafe : But if the Pulley had been of 
24 Inches Diameter, the Diameters of the Rope and Pin being as in the 
fmall one, 45 Pound would have been a fufficient Addition to the Power to 
enable it to give Motion to the Weight by overcoming the Friffion. It is 
therefore well worth confidering the Quantity of Friffion in order to dircft 
us in Praffice } fince in this one Inftance by only ufing a Pulley-Wheel of 
24 Inches Diameter inftead of one of 3, the Force to overcome the Fric- 
tion is left by the Quantity of 391 \ Pound ; oriels than l T of the Power 
added to it will bring up the Weight, when in the other Cafe there muft 
be more added to the Power than one half of it. 

The Axis in Peritrochio has but little Friffion if the Wheel be large and 
the Axle fmall, except what arifes from the folding of the Rope round the 
Axle if a large Rope be made ufe of to raife a great Weight. But yet 
we lhall fliew how to find the Friffiombf the Axle, whatever it be, after 
we have taken notice of the Friffion of the other Machines in general 

The inclined Plane is not liable to much Friftion, if the Weight which 
is roll'd up be fpherical or cylindrick ; for then the whole Friftion -arifes 
only from what the Plane wants of perfect Hardnefs, fo as to fuffer the 
Body rolling up to fink a little, which alters the Inclination of the Plane 
in that Place by making it fteeper, and renders the Line of Direction a 
little inclined to the Plane : So likewife, if the Plane being hard, the Bo- 
dy yields and alters its Figure a little; then it muft be lifted at every 
Pull, or go up by jumps. But if the Body to be drawn up be flat, or qf 
any Figure not fpherical or cylindrical, as a Piece of Timber, or at leaft a 
Sledge loaded, then the inclined Plane will have a great deal of Friffion j 
which we lhall fliew how to eftimate. 

^ The Wedge has a great deal of Friffion 5 for befides all this laft men- 
tiGifd Friffion of the inclined Plane when flat Bodies Aide againft one ano- 
ther, there muft be added the third Part of the Preffure which the fame 
Body gives more to the Wedge than the inclined Plane, by reafon of the 

T Obliquity 



I 



A Comje of Experimental PhiJofophy. 



Amiotat. Obliquity of the Draught, a Wedge being only an inclined Plane with the 
ht&. III. Line of Direction parallel to the Bate, inftead of being parallel to the Hy« 
W^^V^w potenufe of a Triangle, whofe Height is the Thicknefs of the Wedge. 

N..B. IVe do not here take notice of the Cohefion of the Wood or Bodies 
to be cloven, becaufe the Refiftance there to be furmounted is to be con- 
fiderd as a Weighty and therefore attributed to the Weight and not the 
Power. 

The Screw has a Fri&ion of the fame Nature as that of the Wedge, 
becaufe it is compounded of a Wedge 3 but greater, becaufe it touches in 
all its Parts at once, which a Wedge does not ## . The flat or fquare threaded 
*-PIai.F.n. Screw* reprefenting only a fingle Wedge rifing in the Direffion HK or 
fPi.11.R14.LM, has lefs Friffion than the iharp-threaded Screw f; becaufe in 
this laft the Surface of the Thread of the Screw is inclined to the Bafe as 
*>J&u R13. well as to the Axis or Arbor of the Screw. But the endlefs Screw.* has 
yet more Fri£Hon than the fliarp-threaded common Screw, becaufe it is 
oblig'd to take obliquely the Tooth of the Wheel which it drives. 

For this reafbn in Clock or Watch- work thofe that would change 
Wheels and Pinions into endlefs Screws fliould be aware of the great Fric- 
tion that is in them, and not make ufe of them unlels the Nature of the: 
Movement requires it, and there be more gain'd by the Alteration of the 
Uire&ion of Motion than is loft by Fri&ion. 

To fettle fuch a Theory of Friftion as may ierve to direfl: our Praflice 
<|:hat we may not only make a juft Eftimate of its Quantity in every fimple 
Engine - 5 but alfo find out the Fri&ion of the feveral Parts which make up 
^compound Engine, lb as to enable us to know what to allow for the 
. IFri&ion of the whole complex Machine) depends upon fo many Experi- 
Wimts and Obfervations, that I rather choole to confider that Subjefl: in a 
hefture on purpofe (viz. the 4th LeBure) than go on with it here, which 
would Iwell thefe Notes to too great a Bulk fo much remaining to be 
confider'd in relation to the feveral Particulars of the 3d Le&ure, that they 
will far exceed the Length of the Lecture - 7 unlefs I were to omit lome 
Things very material, which yet are too difficult to be mentioned in the. 
hettures themfelves, which I have made fo eafy as to require only the 
Reader's Attention, without any previous Knowledge of Mathematics. 

4. ^20.— — The Beam hanging freely on its Center of Motion, which is 
flafd a little above its Center of Gravity^ As no Pofition of the Beam, 
of the Balance but the horizontal can make us judge of the Weight of the 
Bodies to be compared by that Inftrument, we muffc be careful that the 
Center of Motion or Point of Sulpenfion of the Beam be not in the Cen-? 
ter of Gravity, becaufe then not only the Beam would remain in any gi* 
%6> z ven ; Portion* (^s well inclined as horizontal) but alfo continue in that Po- 

Tb^j 0iB:ly f peaking y the Trillion of Bodies of the fame Weight does not encreafe in 
Proportion to the Number of Parts that rub ; yet it fo happens here, %ccaufe in this Cafe the 
whhmg Surfaces apply- lefs epcatlly to one mother than , in the Wedge* 



A Courfe of E&perimmd Th^ph^j. i 

titioti when equal Weights are fulpended at its Ends. To illuftrate this, Annotaft 1 
let us examine the ift Figure of Plate 14. f Left. III. 

A Cb D reprefents the Section of a Beam of fome Thicknels, which tyv^° 
when fufpended by its Center of Gravity K, will as well remain in the in-+ pl - 
clin'd Pofition AEBF as in the horizontal Pofition : Now if the heavy 
Bodies P,W (equal, if the Body be equally divided in its Length by the 
Point K, or reciprocally proportionable to the Brachia if the Beam be 
unequally divided) be fufpended at the Ends A, B, they will hang in Mqui- 
iibrio in any Inclination of the Beam, let the Beam be of any Size whate» 
ver. Firft, let the Beam be fuppos'd fo flender as to have little or no 
Weight in comparifon of the Bodies, as the Line AB with its Center of 
Gravity at K \ it is evident that the common Center of Gravity of P and 
W, which is at G, will not be fenfibly remov'd from the Point G by thei 
Addition of the Beam ftppos'd of little or no Weight, nor by the Remo- 
val of the Bodies to />, w y when the Beam is inclined into the Pofition 
ab*.- Secondly, if we confider the Beam with all its Weight j when in*L. 
the horizontal Situation CD, the heavy Part CB preffing upon AB being 3^ $$. * * 
equal and equally diftributed over the Beam, and the lower Part AD e- 
qua! to CB hanging under in the fame mariner as CB preffes above, the 
Center of the Gravity of the Beam will not on that account be removed 
from the Point but the common Center of Gravity of the Bodies P,W$ 
and the Beam will be remov'd from G to g under the Center of Motiori 
K 3 therefore the Balance and Weights will remain in that Pofition, ' be- 
caufe the Point & of the Line of Direction is fupported |j ; Neither will J| L. ID 4 * 
tha Weights (which in a Balance always hang freely) be able to alter thi^ 
horizontal Pofition by their Sufpenfion, becaufe their Diftances AK, BK 
from their Lines of Direction to th6 Center of Motion K (upon which 
their Velocities depend) are equal or reciprocally proportionable to their 
Maffes*. Now ir the Beam be inclin'd in the Pofition E AFB, we may*L.II. ip 
ftill confider in it the flender Beam AB loaded above and below with the and L - 
two equal Prifmatical Wedges A F B and A E D, whofe Centers of Gravity 18 a ** d 2ie 
being at ^and », their Lines ofBiredion will go through the Points rand 
s equally diflarit from the Center of Motion K, therefore they will balance 
each other f, and confeqnently not alter the inclin'd Pofition of the Beam. + it 
Then if we confider the Weights p and w fufpended. from the Points a and 
b, the common Center of Gravity of the Beam and Weights will ftill be 
at g, and the Diftances of the Lines of Diredion of the Weights now be- 
coming /K and uK decreafe exactly in a reciprocal Proportion to the 
Weights 5 fo that there can be no Motion oceafion'd by this Pofition of 
the Beam and Weights, becaufe there is no Alteration of Place in the 
common Center of Gravity of the whole loaded Balance, or the refpeaive 
velocity of the Weights. 

But if we remove, the Center of Motion or Point of Sufpenfion of th» 
Balance to^ k a little above the- Center of Gravity of the Beam K, the 
Line of Diredion, which in the horizontal Pofition of the Beam is k g^ 
in the inclin'd Pofition? of the Beam be out of the Point of Sufpen- 



1 40 A Conrfe of Experimental Philofophy. 

"Anhotat fion, which will then be remov'd to c 7 and the Center of Gravity mi? ft move 
Left. III. from g to q 7 which ic can do defcribing a (mall Arc round the Point c\ 
kWNj which will reduce the Beam to an horizontal Pofition, in which the Line 
of Dire&ion will be cq going through the Point of Sulpenfion c 9 and con- 
fequently Weights that are in yEquilibno upon a Balance whofe Center of 
Motion is above the Center of Gravity of the Beam will reduce the faid Ba- 
lance from an inclined to an horizontal Pofition. 

Now in fixing the Center of Motion of the Beam above the Center of 
Gravity, Care muft be taken not to fix it above the Points of Sulpenfion, 
as fome Authors have taught, ani as the Practice is in making the 
common. Scale-Beams, which may be confider'd as made up of two Lea- 
vers making an obtufe Angle at k the Center of Motion, whilft the Points 
of Sulpenfion A, B, are under its Level in the Line AB. Such a Ba- 
lance is us'd for common Pprpoles, becaufe it comes looner to m JEquili- 
hrium^ than if A k B was one Line \ but it is a falfe Balance ', and a skil- 
ful P erf on may cheat with it in proportion as the Angle AkB is more acute r 
flfi.i^'F.i.efpeciatty when there is no Perpendicular Piece or Examen as Cr* t to Jhew 
when the Balance is truly horizontal •> for unequal Weights may make an 
^Equilibrium on fuch a Balance ^ and not be difcover'd by changing the Scales^ 
which prefenfly difcovers the Cheat in a Balance whole Beam has its 
f «7t Brachia unequal -{;. For example, let the Balance A CB^ (whole Center 
■of Gravity is at c and Center of Motion at C with the equal Weight . P,P,, 
hanging at its Extremities A B) be placed in the inclined Pofition ab 7 I 
fay that as the Line of Direflion Dd of the Weight P is brought nearer* 
to the Center of Motion (viz. to q^) the laid Weight may be increased in 5 
proportion as its Diftance Cu is diminifh'd by being reduced to Cq r and 
ad with the very lame Force on its Point of Sulpenfion :. Whilft the Line 
of Direction of the oppofite Weight P being remov'd from D d to b 
Diftance Co becomes Cb r and therefore P may be dimini&'d in propor- 
tion: as its Diftance is increased - therefore in? that Situation of the Ba- 
lance the Weights P and P will keep each other in JEquilibrio^ when they 
differ in the reciprocal Proportion of their . Diftances q€ and bC 7 or bC 
and C^ if the Balance be inclined the other way in the line the Dis- 
covery being only made by the vifible Inclination of the Examen towards. 
s. or t.. E~ D> 

The nearer the Center of Gravity of the Beam is to the Center of 
Motion, the nicer will be the Balance, becaufe the Beam will be the more: 
*:ft.i4,F 9 2,apt to vibrate quick from Side to Side. As- for example,, if acbC* be? 

the Beam and, C the Center or Axis of Motion, the Difference between* 
the Effect of having the Center of Gravity at K, or c, will be the lame 
as. if we. compar'd, the Vibrations of two Pendulums of die Lengths CK 
and Cc x whole Velocities in. their Vibrations reciprocally are in a fubdu- 
glicate Ratio of their Lengths (as I. fliall further fhew when I. corns: 
to treat, of Pendulums) for the Beam is- really, .a Pendulum. 



E x P E« 



A Courfe of Experimental Thilofophy. i±i 



Annotat.' 

ExpiRiM en t. Tlate 14. Fig. 3. 

To the Beam A B, whole Axis of Motion is C, fix a fcrew'd Wire K c pi 14 f s 
and a Ball W fo contriv'd that it may be fcrew'd on towards, or fcrew'd 
frontwards the Axis C. When by bringing the Ball to W the Center of 
Gravity is at K, • the Vibrations of the Beam will be quicker than when 
the Center of Gravity is brought to k by lowering the Ball to w. <this may 
be ufed in P raff ice for fome nice Experiment s r becaufe by fuch a Contrivance 
the Center of Gravity may be brought as near as you pleafe to the Center of 
Motion. 

N.B. That the Center of Gravity ought never to be above the Center L. 2. zm. 
of Motion appears from what has been already faid in the fecond Leclum 
No. 2<<» 

5. [27. In all theft ' Cafes ■ we * fuppofe the Weights to Bang freely from* 
the Ends of the Balance to which they are faften'd.'] Though in 
the common Ufe of the Balance the counterpoifing Weights, or the 
Scales, generally hang freely ; yet there are lome Cafes where they do 
not 5 and in compound fcngines where Balances are often a Part of a com- 
plex Machine ; inftead of Weights, Powers are applied to their Ends in 
all manner of Directions, and then they become Leavers of the firft kind 
fuch as the Regulators in feveral Water Engines, Beams to blow Bellows, 
&c. Therefore I fhall confider the Effects of Powers applied obliquely 
to a- Mathematical Balance or ftreight inflexible Line, which will alfo folve 

a !! 9^! „ of , the Leaver > and (with proper Allowances) may be applied to 
all the Mechanical Organs. 

Let the Balance A B *, I2 Inches long and equally divided by its €en-*Pl. 14.F4* 
ter of Motion C, ftftam at its Ends the two equal Weights W P which 
laft we Hiall confider as the Power. Whilft the Power draws in the Line 
B P, it acts according, to its whole Intenfity-}:, its Diftance being then. r „ „ 

u ™ the Dlftance of the Weight, both Diftances being meafured 
upon the Beam : But if the Power be removed to P, and (its String BxP 
running oyer the Pulley *), it draws obliquely in the Line B x, which makes 
mth the Beam the acute Angle CBF, or (what comes to the fame) the 
obtufe Angle C B E (becauft here we fuppofe it as much greater than a 
right Angle as CBB is lefs,C B F being = CB?) the Force of the Power, 
will be diminim d in proportion as C F or C <p the Diftance from the Line of 
Direction of the Power acting obliquely is lefs than CB the Diftance : of 
the Line ot Direction of the Power acting directly or at right Ancles to 
the Brachium of the Balance CB.*. Knowing therefore the Intensity of * 
the Power which acting at right Angles at B (or which hanging freely 2 °' 
from B, if an heavy. Body, as reprefented here, be the Power) keeps the 
oppofite Weight W in JLquilibrio, one may eafily find how much the Power. 
muft.be enereasd to keep the: faid Weight in. Mquilibrio when it draws 

obliquely^ 



I 




Qmrfe of Experimental Philofbphy. 



Annotat obliquely in any known Direaion, as for example in the Direaion repre* 
tUfa. IlLiented in the Figure ; or (which is all one) how much the Weight P 

.W^O !! h0 ^ n "S -to B runs over the Pulley *, muft be greater thart 

the Weight P which hangs freely to have the fame Effect. With the Di- 
stance Cf or C? draw the Arc F/? which cuts CB at /; then you will 
have the Quantity of P by this Analogy. X 

^ ^3 th . C f \ u P° n the Beam, whofe Length is 4, 8 Inches : 
V to LB the whole Brachiura of the Beam, here 6 Inches Ions :: 

Sots the Intenfity of the Power, or the Weight P here Cuppas' 'd 40 Pounds i 
To the new Power ; ot • Weight P 9 50 Pounds. 

Hence it appears that the Weight P thus found, would keep the conn- 
terpoifing Weight W in Mquilibrio by hanging freely at the Point L as 
well as it does ^it by drawing obliquely over the Pulley x : becaufe the 
Momentum of W (or W x A C) being divided by C /, will give the Quan- 
tity of the Weight P ; or, in other Words, there will be a reciprocal Pro- 
^ C i° n Jf tWe 5 n the Wei S hts w Py and their Diftances CA and 
IPf, IF o ? f ' ™ erefore C/= C<p = C F the Diftance of the Line of Direftiort 
«, « and*™™ the ? ent 5 of Motion (*l™ys found by the Length of a Perpendicu- 
» lar from that Center to the /aid Line of Direction) may in all fuch Cafe 

be properly call'd the acling Difiance of the Power, See No. 20. 

Another Way. 

Through the Point x taken in the Circumference of the Pulley, over 
which the String BxP runs, draw x E parallel to the Balance A B, which 
will cut the perpendicular Line of Direction of the Power (or freely hang- 
ing Weight) P, at right Angles at D, D *. being - DE, and the Angle 
xB D = DBE by Suppofition. In the rectangular Triangle BDx, as 
much as the Hypotenufe Bx is longer than the Perpendicular BD, fa 
much muft the Quantity or Intenfity of the Weight P (which hanging free- 
ly keeps W in ^Equilibria beincreas'd when it draws obliquely in the Line 
B a? j that is, fo much muft P be greater than P to keep W in Mquili- 
brio drawing obliquely. The fame would be true if x was remov'd to E;.. 
and therefore this will always be the Rule to eftiraate the Force of Powers 
drawing obliquely. 

As the Sine of the Angle of Trailion, viz. the Angle which the Line of Direct 
tion of the Power makes with the Beam : 

Is to the Radius : : 
So is the Intenfity of the Power drawing at right Angles with the Beam : 

To the Intenfity of the Power drawing obliquely. 

N.B. The Angle of Traaion here is CBxorCBE y whofe common 
Site is BD| then in this Cafe BD :-B* P :■ P» 

That 




A Courfe of Experimental Philofophy. 

That this Method will always have the fame Confequence as the former, Annotat. 
may be leen by comparing together the two Triangles B x D and CBF}Le£l. IIL 
for fince CFB is a right Angle by Supposition, and CB* = B*D be- KSV~\S 
caule of the Parallels C B and x D, BCF rauft be equal to,*BD and 
confequently the Triangles be fimilar, which will fhew that CF (48) • CB 
(60) : : B D (40) : Ex ( 5 o) : P : P. §K E. D. ' 

This might alio 'be explain'd a third Way, by refolving the Force which 
draws obliquely in the Line Dx, into the Forces, the one drawing along the 
Leaver in the Line B C, and the other in the Line B D, after Sir Ifaac 
Newton's Manner*; but we mall confider it in the Cafe of Trufion or* .$« m 
puihing obliquely againft any Point of the Beam, which is the fame as ' 
drawing the contrary Way. 

All thefe Methods will appear to agree in the following 

E x p e r 1 m e n t. Tl. 14. Fig. 5„ 

The Balance or Leaver A B, 12 Inches long, is moveable upon the 
Center C of the Stand S, which has a long Piece fo propp'd at S as *to 
remain in an horizontal Pofition, fo as to carry the Pulleys x and E, each 2 
Inches diftant from the Point D which is placed perpendicularly under B. 
When the Power P of four Ounces equal to W hangs freely, it keeps W 
in- ^Equilibria , but if the String PX B be thrown over the Pulley x or E 
then will the faid Power P be overpois'd by W till it be changed for P orp 
a Five-ounce Weight, which drawing obliquely over x or E will keep W 
in Mquilibrio. Now one may obferve, that when P defcends one Inch or 
from P to r, it brings down the End of the Beam B only to the Point 
b m the horizontal Line fe, which raifes the oppofite End A to a ■ iuflf- 
as' high-above the Line AB ; but when the Power at P delcends one 
Inch, namely to q, it brings down the End B to 6 in the horizontal Line 
bg, and confequently raifes the oppofite End A fo much higher, fo as to 
give more Velocity to the Weight W bringing it to w inftead of w. Now 
fince the Powers F and P with the fame Velocity (or defcending equally); 
give : W difierent Degrees of Velocity, their Intenfities mult be different 
in that Proportion, becaufe Caufes are always proportionable to their Efetls - 
therefore P muft be greater than P as much as the Arcs A » and B ft are' 
greater than A a and B i>, or rather as much as the Sine tt 0 is greater' than • 
an. Th,s alfoappears^by observing (fince BX = Hx ( =JW ) andB^) that 
the Strings B P, B * P, and 0 * P q are all equal. 

N.B. rhis is Jlri&ly true only in the Beginning of the Motion of the Beam; 
but that ts fufficient for our Purpofe. 
; ; The : very Sight" of the Machine makes it plain that a Power adine atr 
right Angles is the moft effeftual. For as in removing the Power from- 
the Perpendicular it draws^more weakly at E, and at m it only pulls the 
Center C in. the Bireaion B m fo as to do nothing towards raifing A the 




H4 

Armotat. oppofitc End of the Beam j and going the contrary Way, the Power wea- 
Lea.JIL.kend at x, becomes wholly ineffectual when brought to the Beam to draw 
in the Direction BC, becaufe then it only ads againft the Center C no Way 
moving the End A : Therefore a mean Situation of the Line of Direftion 
between thole two ineffectual Extremes, muft be the moil effeftual • and 
that is in the Line B P perpendicular to the Beam. 9 

It is upon this Principle that mo ft of the Feats of the pretended ftrong Men 
or modem Sampfons are performed \ the Machines on which they fit or ftand 
being fo contrived that the 'drawing Horfes or hanging Weights pullthofe Limbs 
of the Man refifting (which perform the Office of a Leaver or Balance) in fuch 
a manner that they are drawn directly againft the Center of Motion. But 
this I fhall explain more particularly when I come to fpeak of thofe Feats 
of Strength. 

If at one of the Ends of a Leaver or Balance be ftx'd a Weight, which 
(moving with the [aid End of the Leaver) does not hang freely \ whilft the 
Power a&ing at the other End is either a heavy Body hanging freely, or an 
animate Power prefftng perpendicularly towards the Earth 5 / fay, that fuch 
a fix'd^ Weight will vary in Force according to the P oft t ion of the Beam, and 
that Force will vary in a contrary manner according as the Center of Gravi- 
ty of the Weight is above or below the Beam % namely, when the Center of 
F.tf. Gravity of the fix'd Weight is below the Beam (as in Fig. 6.) the Weight 
will become heavieft (or adl moft ftrongly) when raised above the horizontal 
Line (as at G) in the inclined Situation of the Leaver DCG} and it will 
become lighteft when deprefs'd below the horizontal Line {as at E) in the in- 
clined Situation of the Leaver A CE 5 on the contrary, if the Center 1 of 
PL^F-j. Gravity of the ftx'd Weight be above the Leaver (as in Fig. 7.) it will be- 
come ^heavieft when deprefs'd below the horizontal Line {as at K) in the 
inclined Situation of the Leaver ACK; and become lighteft when raised 
above the horizontal Line {as at E) in the Situation of the Leaver D C E . 
But the faid fix'd Weight will aft in the fame manner as if it hung freely 
when the Leaver is in the horizontal Situation as at BF (Fin. 6*S and 
BI (Fig. 7 .) . * ' J 

PL 14. F. 6. The firft Cafe (Fig. 6.) may be thus explained. In the Po&ion of the 
Leaver B F, the Line of Direction q O going thro' the Point of Sulpenfion 
* See Page h and be5n g at right Angles with the Leaver, Cq is the ailing Diftance*, 
I4 2 9 of the Weight as well as the Diftance of the Point of Sulpenfion ^ there- 
fore as BC : to Cq : : fo is the Weight F : to the Power R • in the fame 
manner as if the Weight F hung freely from q. But when the Weight 
is rais'd up to G, as the Center of Gravity O cannot get under the Point 
K (the fame as q the Point of Sulpenfion in the horizontal Leaver) Or 
becomes the Line of Direftion inftead of K M which would have been 
the Line of Direction if the Body had hung freely from K ; therefore 
Cr is the affing Diftance of the Weight inftead of C M, when the aaing 
Diftance of the Power is become LC-, and confequently the Weight has 
more Force, and can only be balanced by a greater Power as P. For 
whereas CL : CM :: F (or G) : R, now CL : Cr :: F (or G) : P, 

from 



A Courfe of Experimental Phihfophy. 145 

a Stronger Power or heavier Counterpoife. But if the Weight be brought Anriotac 
to H, its Line of Diredion inftead of nH becomes MO, and confequently Lte& Ill, 
its ading Diftance is lefs than it ought to be in Proportion to C Q the o^v*sj 
acting pittance of the Power, which therefore may be diminiih'd in Inten- 
fity and become S inflead of R. 

From what has been faid, and a View of Fig. 7. * one may fee that the * Pi- 14. F- 7« 
contrary muft happen when the fix'd Weight has its Center of Gravity ' 
above the Leaver or Beam. For in the Situation of the Leaver E D, the 

•f j r^? 10 L° f the Wei & ht comin S forward too faft (becoming O L 
mftead of Eh) C L the affing Diftance of the Weight at E bears a lefs 
Proportion to C N the afling Diftance of the Power at S, than Cg to C B 
the Proportion in the horizontal Situation ; and confequently the Power S 
of lefs Intenfity ferves as a Counterpoife inflead of R. But when the 
Weight is deprefs'd to K, we muft make ufe of P a greater Counterpoife ; 
becaufe Cg is become the afting Diftance inflead of Ct. And in the ho- 
rizontal Situation of the Beam the Body O weighs the lame as if it hung 
freely becaufe is its Line of Direction, as it would be if the faid Body 
hung down from g. This may be obferv'd in Practice. Suppofe the Man 
M {.Fig. 2.) is lifting Hay, Sheaves of Corn, or a large Faggot A byw T „ w « 
means of the Prong or Fork AB refting upon his Knee e as *Fricrum\vk 4 ' 
preffing down the End B of the Prong or Leaver } if the Fork A goes un- 
der the Faggot, it will be the Cafe of the inclin'd Leaver A K {Fig. 7 .) P1 Tyl » , 

fl Bl ' rt f en Wl11 S row li & hter as ic rif es- But if the Fork had been 4 ' 7 " 
thruft through the Binding above the Faggot, it would be the Cafe of 
the mchnd Leaver A E (Fig. 6.) at whofe End the Burthen. becomes P , u F « 
heavier as it is rais'd up; and then if the Man was juft able to begin to 4 
lift it, he muft let it go back again, or find a new Fulcrum as C in or- 
der to raife that Weight. Suppofe again, that the Beam of a large Pair 
of Scales, was mchn'd in the Pofition ACE ; a Man in the Scale fuf- 
pended at H [may, by thrufting up his Hand hard againft the Beam, 
put hiiufelf in the Condition of the heavy Body HE, and confequently 
appear to weigh, lefs than his true Weight, being counterpois'd by fuch 
a Weight as S But if the Scale which he gets into be rais'd up, its 
Point of Sufpenfion being at K in the Pofition of the Leaver DCK • the 
Man by thrufting _ hard againft the Beam above his Head, may throw his 
Body into a Pofition perpendicular to the Leaver, and together with the 
■Scale be m the Condition of the Body KG; fo that if there is more 
Weight in the oppofite Scale, the Weight need not be leffen'd till its In- 
tenfity be equal to that of the Man's Weight, but it will begin to be 
lifted up whilft it is ftill greater j fo that in fuch a Cafe, a Man's Weight 
will appear greater than it is, by as much as the Counterpoife P° is 
greater than R. Juft the Reverfe would happen, if a Man was to fit upon 
the Beam } for then he would weigh leaft, when rais'd above the hori- 
zontal Line going through the Center, as at EM (% 7.) and raoft pi IA p , 
when below the faid Line, as at F K. ' 4 ' F ' 7 * 



Now 



A Courfe of Experimental Philofophy. 



Annotat. Now tho' the Action of heavy Bodies on one another may thus in the 
Led, III. Balance and Leaver and Tome other of the Mechanical Organs be eftima- 
t/YV ted by the Diftance of their Line of Direction from the Center of Mo- 
tion \ yet this is only fo far true, as the perpendicular Alcent and Defcent 
is agreeable to that Diftance V for there are Cafes efpecially in the work- 
ing "of compound Engines, where the Diftance of the Line of Direction of 
a rifing or falling Body from the Center of Motion is not proportionable 
to the perpendicular Afcent or Defcent of the faid Body. Therefore the 
Velocity of a Power, when it is an heavy Body, muft be confider'd in the 
fame manner as that of a Weight - 7 as has been fully explain'd in the 8th 
*L.2.Ann.8.Note of the fecond Lefture * * and may be further prov'd by the fol- 
lowing 



Experiment. 



*Pl.i4.F.$. ACBE-KD* is a Balance in the Form of a Parallelogram paffing 
through a Slit in the upright Piece NO ftanding on the Pedeftal M, fo 
as to be moveable upon the Center-Pins C and K. To the upright Pie- 
ces AD and B E of this Balance are fix'd at right Angles the horizon- 
tal Pieces FG and HL That the equal Weights P, W, muft keep each 
other in jEquilibrio is evident * but it does not at firft appear fo .plainly, 
that if W be removed to V,' being fufpended at 6, yet it ihall keep P in 
MqmUbrio y tho' the Experiment fhews it. Nay, if W be fucceffively mo- 
ved to any of the Points i, r, ^ E, 4, 5, or tf, the Equilibrium will be 
continued'-, or if, W hanging at any of thofe Points, P be lucceffively 
mov'd to D or any of the Points of Sufpenfion on the Crofs-Piece FG, 
P tvill at any of thofe Places make an Equilibrium with W. Now, when 
the Weights are at P and V, if the leaft Weight that is capable to over- 
come the Friaion at the Points of Sufpenfion C and K be added to V as 
,u % the Weight V will overpower, and that as much at V as if ic was 

at W. 

From what we have faid above, the Reafon of this^ Experiment will be 
very plain. As the Lines AC and K D, CB and RE always continue 
of the fame Length in any Pofition of the Machine, the' Pieces A D and 
BE will always continue parallel to one another and perpendicular to the 
Horizon, however the whole Machine turns upon the Points C and K } 
as appears by bringing the Balance to any other Pofition as abed: and 
therefore as the Weights applied to any Part of the Pieces FG a 
can only bring down the Pieces A D and BE perpendicularly in the fame 
manner as if they were applied to the B'ooksDc and E or to X and Y 
the Centers of Gravity of A D and BE, the Force of the Weights 
(if their Quantity of Matter is ;equal) wifl be equal becaufe their Velo- 
cities will be their perpendicular Afcent or Defcent, which will always be 
as the equal Lines s* and 5^, whatever Part of the Pieces F G and H I 
^he Weights are applied to. But if to the Weight at V be added the 



A Courfe of Experimental Phihjbphy. 147 

little Weight u r thofe two Weights will overpower, becaufe in this Cafe Annotat. 
the Momentum is made up of the Sum of V and u multiplied by the Lett. III. 
common Velocity 5 y. v^V""^ 

Hence follows, that it is not the Diftance c 6 multiplied into the Weight 
V, which makes its Momentum; but its perpendicular Velocity 5 y multi- 
plied into its Mats*. ^. E. D. * 4 3 # 

This is ftill further evident by taking out the Pin at for then the 
Weight # P will overbalance the other Weight at V, becaufe then their 
perpendicular Afcent or Defcent will not be equal 

To conclude all that relates to Forces applied in different Dire&ions 
to Learers and Balances, I fhall explain the Aftion of oblique Forces by 
the Compofition and Resolution of Motion after Sir Ifaac Newton's Manner'- 
applying the Solution to a Propofition on the Balance, which has not 
been taken notice of by mechanical Writers tho' often talkM of by handi- 
craft Workmen. 

Theorem- Fig. 10. PU4.F.1®, 

A B is a Balance on which is fuppos'd to hang at one End B the Scale 
E with a Man in it, who is counterpoised by the Weight W hanging at A 
the other End of the Balance. I fay, that if fuch a Man, with a Cane or 
any rigid freight Body, pufhes upwards againfi the Beam any where between 
the Points C and B (provided he does not pufh direBly againft B) he will 
thereby make himfelf^ heavier or overpoife the Weight W, tho' the Stop G G 
hinders the Scale E from being thru ft out fromwards C towards GG. I 
fay like wife, that if the Scale and Man floould hang from D, the Man by 
pufhing upwards againft B or any where between B -and D .(provided he does 
not pufh direffly againft D) will make himfelf lighter or be overpoised by the 
Weight W, which did before only count erpoife the Weight of his Body and the 
Scale. . 

If the common Center of Gravity of the Scale E and the Man fuppos'd 
to ftand in it be at k, and the Man by thrufting againft any part of the 
Beam caufe the Scale to move outwards fo as to carry the faid common 
Center of Gravity to . * ; then inftead of BE, hi will become the Line 
of Direftion of the compound Weight, whofe Adion will be increased in 
the Ratio of LC to BC This is what has been exolain'd by fcveral 
Writers of Mechanicks ; but no one, that I know of, has confider'd the 
Cafe when the Scale is kept from flying out, as here by the Poll G G, 
whiph keeps it in its Place, as if the Strings of the Scale' were become in- 
flexible. Now, to explain this Cafe, let us fuppofe the Length BD of 
half of the Brachium B C to be equal to three Feet, the Line BE to 
four Feet, and the Line E D (of five Feet) to be the Direaion in which the 
Man pufhes, DF and FE to be refpeftively equal and parallel to B E and 
B D, and the whole or abfolute Force with which the Man pufhes, equal 
Mor able to raife) 10 Stone. Let the oblique Force ED' (= x0 Scone) 

U a be 



1 48 A Courfe of Experimental Philofophy. 

Annotat be refohfd into the two EF and E B (or its equal F D) whofe Directions 
Left. III. are at right Angles to each other, and whofe refpeftive Quantities (or In- 

^/TV tenfities) are as 6 and 8, becauie EF and BE are in that Proportion to 
each other and to E D, Now fince EF is parallel to B OCA the Beam, 
that Force does no way affect the Beam to move it upwards ; and there- 
fore there is only the Force reprefented by F D, or 8 Stone to pufh the 
Beam upwards at D. For the fame reafon, and becauie Aftion and Re- 
action are equal, the Scale will be puftfd down at E with the Force of 
8 Stone alfo. Now, fince the Force at E pulls the Beam perpendicularly 
downwards from the Point B diftant from C the whole Length of the Bra- 
chium BC, its Aftion downwards will not be diminilh'd, but may be ex- 
prefs'd by 8 X BC: Whereas the Aftion upwards againft D will be half 
loft, by reafon of the diminifh'd Diftance from the Center, and is only to 

BC 

be exprefs'd by 8 X — h and when the Aftion upwards to raife the Beam 

2 

is fjbtrafted from the Aftion downwards to deprefs it, there will ftill re- 



main 4 Stone to pufh down the Scale j becaufe 8 -X BC - 

2 

4 BC. Confequently a Weight of 4 Stone muft be added at the End A 
to reftore the ^Equilibrium. Therefore a Man^ Sec. pujhing upwards under 
the Beam between B and D, becomes heavier. §K E. D. 

On the contrary, if the Scale fhould hang at F from the Point D only 
three Feet from the Center of Motion C, and a Poftgg hinders the Scale 
from being pufh'd inwards towards C } then if a Man in this Scale F 
pulhes obliquely againft B with the abfolute Force abovemention'd ^ the 
whole Force, for the Reafons before given (in refolving the oblique Force 
into two others afting in Lines perpendicular to each other) will be redu- 
ced to 8 Stone, which puihes the Beam direftly upwards at B, while the 
fame Force of 8 Stone draws it direftly down at D towards F. But as 
C D is only equal to half of C B, the Force at D compared with that at 
B lofes half its Aftion, and therefore can only take oif the Force of 4 
Stone from the Puih upwards at B - 0 and confequently the Weight W at A 
will preponderate, unlefs an additional Weight of 4 Stone be hang'd at B. 
^therefore a Man> &c. pujhing upwards under the Beam between B and D 
becomes lighter. Which was alfo to be demonftrated. 

Scholium I. 

Hence, knowing the abfolute Force of the Man that puflies upwards 
(that is, the whole oblique Force) the Place of the Point of Trufion D, 
and the Angle made by the Direftion of the Force with the Beam at the 
faid Point, we may have a general Rule to know what Force is added to 
the End of the Beam B in any Inclination of the Direftion of the Force 
w' Place of the Point D« 



Ruh 



A Courfe of Experimental Phihfopfy i^p 

„ , . . ■ . Annotat. 
Rule for the firft Cafe. Le g. # m 

Firfl: find the perpendicular Force by the following Analogy, whofe 
Demonftration is known to all that underftand the Application of oblique 
Forces. 

As the Radius : 

to the right Sine of the Angle of Inclination of the Force to the Beam %x 
So is the oblique Force r 
to the perpendicular Force. 

Then the Perpendicular Force multiplied into the Length of the Bran- 
ch ium BC, minus the laid Force multiplied into the Diftance DC, will- 
give the Value of the additional Force at B, or of the Weight requir'd to 
reftore the ^Equilibrium at A. 

Or to exprefs it in the Algebraical Way. Let of exprefs the oblique 
Force, pf the Perpendicular Force, and * the Force requir'd, or Value 
of the additional Weight at A to reftore the Mquilibrium. 

DE : D F (= BE^:£«/ : pf. 
^73TB^— pf * DC^ #. 

The fame Rule will ferve for the fecond Cafe, if the Quantity found' 
be made negative, and the additional Weight fufpended at B. Or having- 
found the Val ue of the Perpendicular Force, the Equation will Hand thus r. 

w^u* B f j" 1? ?1 D C - - a • and confequently the additional? 
Weight muft be hang'd at B ; becaufe — x at A is the fame as 4- » 
at B» s 

Scholium 2. 

Hence it follows alio, that if, in the firfl Cafe, the Point of Trufion Br 
taken at C, the Force at B (or Force whofe Value is requir'd) will be the 
whole Perpendicular Force •, becaufe C D is equal to nothing : And if the 
Point D be taken beyond C towards A ; the Perpendicular Force puih- 
mg upwards at that Point, multiplied into .DC muft be added to the fame 
Force multiplied into BC, that is pf >cBC -f pf'yTUC ' - 

The Machine Imadeufe of to prove this experimentally, was" as follows. 
{Fig 11.) The Brais Balance A B is 1 2 Inches long, moveable upon the PI ntFn 
Center C, with a Perpendicular Piece Bb hanging at the End B and mo- 
vable about a Pm at B, and ftopp'd at its lower End b (by the upright 
Plate GG) from being thruft out of the Perpendicular by the pining, 
I ipe F fe, whole lower Point being put into a little Hole at H, the up! 
per Wire or Point (when put inco another little Hole under the Beam St 

D) is* 




Arinotat. D) is by means of the Worm-Spring E F preffing againft the Plug E to 
Left. III. drive forward the faid Wire h D, made to pulh the Beam upwards with 
tA^ 1 the Force of the Spring EF TSS is a Stand to which is fix'd the Pillar TC 
which fuftains the Balance*, arid it has alfo a Slit SS to receive a Shank 
of the moveable Pliite GG, to be fix'd in any Part of the Slit by a Screw 
underneath. 



Exp e r i m e n t. TL 14. Fig. 1 1. 

Hang on as in the Figure. Then let EF be fo applied to the 
Hole H, that its upper Wire hDk may go through a little Loop at D, 
fo as not to thruft the Beam upwards, but be in the fame Pofition as if 
it did, that by hanging on the Weight W the Brachium GC with Bb and 
F E may be counterpois'd, that the Adion againft D and H may be efti- 
mated without the Weight of the pulhing Pipe. 

Then drawing down the End of the Wire k thruft it into the little 
Hole under D, and B will be 16 piilPd downwards as to require the ad- 
ditional Weight . P of 4 Ounces to be hung on at A, to reftore the Mquili- 
brium\ When BH is 4 Inches ; BD 3 Inches, and the whole Force of 
the Spring equal to 10 Ounces. 

I need not here fay^ that for explaining the fecond Cafe, B b is to be 
fufpended at D, with the Plate GG fix'd to ftop it at the Place M to 
keep it from being pufh'd towards T, and that the upper End of GFED* 
muft pulh into an Hole made under B, in which Cafe the Weight P 
muft be hangYl at B to reftore the Mquilibrium. 

B. To fhew experimentally that the Force which the Spring ex- 
erts in this oblique Trufion is equal to ic Ounces : Take the Beam AB, 
which weighs 4 Ounces, from its Pedeftal C T, and having fufpended at 
each End A and B 3 Ounces, fupport it under its Center of Gravity by 
the pulhing Pipe EF fet upright under it, and you will find that the 
Beam with the two Weights will thruft in the Wire R£ as far as the 
Place which the oblique Trufion drives it to. 

6. [29. — In all thefe Cafes the Liaver is f ill faid to be of the firfi Kind^ 
There is another way of diftinguifliing the Leavers according to Ariflotle 
and the Mechanical Writers among the Ancients 5 and that is as the 
Weight does, or does not, rife in the fame Direction as the Power, As 
for example, in the Leaver of the firft Kind j as it has the Fulcrum (Cen^ 
ter of Motion, or Hypomochlion) between the Power and the Weight, the 
Power muft move downwards wJiilft the Weight moves upwards j and that 
Leaver is by thole Authors calfd the Heterodromous Leaver- that is 5 
'working ot ' moving , different " Ways. But the Leaver of the fecond, and like- 
wife the Leaver of the third Kind, are both calVd Homodromous Leaver^ 
becaufe the Power and Weight being on the fame fide of the Hypomoch* 

lion 



A Courfe of Experimental PbiJofophy. i § i 



lion or propping Point, they both go the fame Wa^ ? tho' in the one the Annotat 
Power always gains, and in the other always lofes. Led- HI* 

If we examine fuch Instruments as we have in common Ufe, we may ^*S~\/^\J 
plainly lee that they are Leavers of one of the three Kinds. As for ex- 
ample, a Pair of Pincers* is made up of two Leavers of the firft Kind,* Pl.t 4 ? F.i2 e . 
whole common Center of Motion is at the Rivet C, the Power being ap- 
plied at the Handles Bb to prefs them together, and thereby pinch the 
Body D as a Weight at theoppofite Ends Aa, in which Cafe the Power 
a£ls fix times more ftrongly than if applied dire&Iy to the Body D at 
A, a-j fince in the two Leavers A B and ab the Diftance of the Power 
BC and bC is triple the Diftance of the Weight C A and Ca. So is a 
Pair of ScifTors <\ made up of two fuch Leavers, whole common Center 0ffpj.14iF.13.. 
Motion is C, the Power being applied at Bb, and the Body to be cut as 
a Weight at D where it is evident that the nearer D is to the Points 
A a, the greater will be the Difficulty in cutting it 5 and the le&, the near- 
er it is brought to C. The Force of a Leaver in this Way is remark- 
able in the Brafier's or Tin-man's Sheers*, whereby one Man prefling up- *pi. 14,^14-. 
on the Handle B raifing the lower Sheer A C, moveable about the Cen- 
ter C, is able to cut a Plate of Brafs or Copper D a quarter of an Inch 
thick, the other Sheer a C E being riveted to a couple of ftrong Standards 
fix'd into the Block F. Nippers, Forceps, Snuffers and other fuch In- 
ftruments may in the fame manner be found to be Leavers of the firft 
Kind. The little Cart or Carr B C A * very ufeful in Building, is alfo*PLi 4 .F.i 5i ~ 
a Leaver of the firft Kind : It is made to lift great Stones and carry them 
to the Builders $ upon the farther End of whofe Plank or Bottom A 
the Stone D being laid, and with a little Pains mov'd towards C by wrig- 
ling the Plank \ the Force of one Man by taking hold of the long Handle: 
at B, and weighing it down as it turns about the Axle-tree of tjie Wheels* 
EE" as the Fulcrum, will be able to raile that Stone ; and being rais'd, by 
Help of rhe Wheels, be able to convey it to the intended Place. 

The cutting Knife * us'd by Druggifts and Patten-makers, to cut Drugs/ PI.hF.i^- 
or the Wood they ufe, is moveable on the Joynt or Center of Motion C, 
whereby it is faften'd to the Plank C E ^ the Power is applied at* , the 
Handle B, and the Weight is D the Wood or Drug to be cut: This : 
Ihews the Inftrument to be a Leaver of the fecond Kind •{% So is a Dpor,f 30^ 
whole Hinges are the Center or Axis of Motion, the Hand or > Power be- 
ing applied at the Part to wards the Lock, whilft the ./Body of the Door 
is the Weight. A Pair of Bellows are two Leavers of the fecond Kind,, 
whofe common Center of Motion is at the End of the Boards where ,the 
\Nefe begins, the Power being applied at the Handles, whilft the Air to- 
-be prefs'd put between the. Boards, by its Refiftance afls againft the . mid- 
dle of the Boards as a Weight. 'Thus pne may eafily perceive that ; ^he- 
Latch of a Dc^or, when drawn up by a Striog, is a Leaver f of .the ...fecond* 
Kind} as are^'llb jointed^Nut-crackers, Horferbarnacles, .'&c. The Oars 
of a»iBoat or Galley and the Rudder . are alio Leavers of the fecpnd Kind, , 
$W <)dtifivtk lupposU them: Leavers of the firft j but the Error lies in* 

this. , 



i §2 A Courfe of Experimental Philofophy. 

^ Annotat. this, that he confider'd the Water as the Weight to be mov'd i whereas 

^JR* » he rS° at or 5 a l ey is the Wei 8 ht ' t0 be mo ' ,d - For the Water makes 
*eT3Tp & e K a v> e ^ at . C as a the M ™ or Power afting at B, whilft the 

* 7 and 18. * T vd , b X £hat Part of Leaver which prefles on it at 

the Point D, as the Oar in Fig. 17. and the Rudder in Fig. -g. But Ari- 
ftotie, in his Mechanics, rightly reckons the Mafts of Ships among Leavers 
of the fecond Kind, alligning the Fulcrum or Hypomochlion to be in the 
•if-.Pl. 15.F. i. bottom of the Ship B -{- confidering the Ship it feif as the Weight or Bur- 
then, refting with its upper Deck C upon the Maft, as upon a Leaver, and 
fo to be mov'd forwards. Laftly he affirms, the moving Force to be the Wind 
gather'd in the Sail, which, by the Help of the Sail-yard, ' is applied to 
A i and chen he gives a Reafon from the Principles hitherto deiiver'd 
why, the higher the Yard DAE is, fo much the fwifter the Sh<*p will 
be earned with the fame Wind and Sail ; viz. becaufe the farther the 
Fulcrum is from the moving Force (all other Things being at the fame 
time conlider'd) fo much the eafier will the fame Power or Force move 
the Weight. ' ' 

The fame Instrument, according to its different Application may be a 

*pi t, 17 „ Lea ^ e f of ^ he firftor fecond Kind : As for example, when a Man who has 
11.14 u.i 5. carried a Stone upon the Carr* goes to deliver it at the Place intended fo 
as to lay it upon its Side E, he lets the End of the Plank reft upon the 
Ground at E, and lifting up the End B turns the Stone over } which 
Operation changes the Leaver from one of the firft Kind into one of the 
lecond, where E is the Fulcrum, B the Power, and the Weight is at A. 

tPl.i5.F.2. The Sheep-fheers -\ are two Leavers of the third Kind; the common 
Center of Motion being at the fpnnging Bow. at C, whilft the Power or 
Hand is applied at Pp, and the Wool to be cut is the Weight at W. 
Thus are the two Legs of a Pair of Tongs vifibly Leavers of the third' 
Kind. A Ladder or a Pole to be rear'd againft a Wall are alio Leavers 
of the third Kind. But the Ufe of Leavers of the third Kind is moft 
beautifully fhewn in the animal Body, where the All-wife Creator has ap- 
plied Animals with a Means to move the Limbs with great Vejocity by ap- 
plying the Power of the Mufcles very near the Center of Motion • but at 
the fame time giving the Mufcles fuch very great Force as to perform 
their Office very fudden.ly, railing the Limbs even when great Weights 
hang at their Extremities \ as for example, when we lift Weights with 
our Hands or Feet, or when we hold or break hard Bodies with our 
Teeth. There is fcarce a Bone in the Animal Body but what is a Leaver 
of the third Kind. It is a delightful and curious Contemplation to con- 
iider what Proportion is obferv'd in the Animal Body as an Engine, from 
which Art only copies faintly : There we may fee various Applications of 
Powers, and how they help each other in moving the Limbs, fometimes 
afting jointly at the fame time, fometimes fucceeding one another to change 
Directions, and fometimes afting againft each other to flop and check Mo- 
tion \ at other times drawing over Pulleys to alter the Angle of Traction 
as need requires. But this Subject is fo copious that we can only give 



one 




one laftanee m two here ; *efef*iag the curioos to ©enfofc Jbkonfits Bo- An^otat 
relU who has written a whole Book upoa that Sufejea (w's. de Metu 4m- Left III 
mdimP) and from phom we 4hajl take only a few Examples. ^& M' ^Ar^S 
lows the lift Propofition of his firflBooL 



"Pro p © <s I f l €> N 

« fffc* ^/ete Power tf every wmal Mufck, mufl neeefflirih %e tpm® 
« than -the Wmht tf the Limb fufteniti by it, hut never left, Plate i?. PI n F.z 
" **g 3> ««d 4 . 5 and J: 

« All-w# Nature has fq contriv'd thethape of Animals made up of 
{evecal Organs joai'd together, as to enable them 10 move from one 
" Place to another, and perform the feveral Operations requir'4 for the 
u Preleiwation .of Life. But this could not be" done %y giving an Animal 
** an -orbicular Shape iijpe a Ball, but it was proper that he fhpuld be 
" made up of feveral Articulations, fijch as Hands and Feet to walk 
« about and handle ©tye&s. But theft Limbs could not move about 
« JoMts, unlefs they were drawn by mufadar Cords, and thofe Cords were 

* ^trafitedky a moving Force. We are going to fhew, that t&t movini; 
vmtc or Power misft not be kfs, font weceffarily greater than the Weight 

« and Refinance of the Limbs fufpeaded. Let" us confider m \mb ' 
« for exampik the whole Avm ; it is .plain that it was neceffary for it to 
" move round every way about the Joynt of the Shoulder, that it might 
« be able tp ^draw , f^fpend, and impel! the M^mmms as wdi of the 

* Weight s pf the Ai-Hi as of external Bodies to fee handled - Such Qpera- 

* mqmt^fx^pt Figut-e, Forces and apt Inflrumencs '\and W fit- 
' ted for that fWf ? , The Shape without Ipubt m $ be long like a 
\ ¥ S ^5 ^We^ft«t.* Cfftfer, or the fix',d Pojtjf ©r firm ,of 
v «« bowlder, fhen jn*he Leaver aift be eonfider'd the Positions in 

* which *he Roving Bower and the Refinance are applied. The moving 

* Power .afts by wratting the mu%Jar £ords, wMeh qan only be 

* ften J »ear the tartf Motion of toer, ,as |a S & een faid be- 
We*y WNtf »e Jiefifcujce *s >applj§d *t its -«tsp<aft Length or farther 

" End,, 

vemoMfy Jhem th^t the Te^to <nye the < let the MtfdeDE ]>e faflju* G Z'&c'd ' 

0e Center cfMot m ^ m m deap<wrt<>d> m « Aw «r Qtbit AM, ,**hkh End mik be 
mzekmed E m >nf n,ar the JrtwM<m ' ^m^ m^the Cent^ of the jirtioalatiL 

*P1. J I5.F,3. Let there be iwMws * A B ^ ,^J^ m ought tz Ufte» the 

ted at AF, namely in fuch manner that AB VAB. For if It couldbe Let us ■fuMde the 
' »»J ke dra ™ ^ C the Center of the Jr. * C*mem m kto h majfnL J £ffw$. 

^" and : 



1 54 ji Courfe of H Experimental Pbilofophy. 



Anno tat. " End * 9 therefore the Power: will always be to the Reftftance \\ as the 
Left. III." greater Difiance of the Refifiance : to the leffer Di fiance of the Power 
" from the fame fix'd Point j conlequently the moving Power is greatec 
u than the Refinance. 



a 



Proposition XXIL 



€£ The fir ft Enquiry of the abfolute apparent Force, which can be excrU 
u ed by the two Mufcles, the Biceps and Brachieus, bending the Cubit (or 
xc lower Bone of the Arm) when the whole Arm is in a fupine and hori- 
€C zontal Situation^ which is greater than twenty times the Weight that is 
a fuftairfd by them, and exceeds the Force of 560 Pound FFeight. Plate 15. 
15. F.4. H Fig. 4. ■ { 

" Let the Humerus EA, and the Cubit and Hand A B, be almoftin 
a right and horizontal Line, but fupine (that is, with the Elbow down- 
wards) and let the Cord G B fold about the Ends of the Fingers of the 
expanded Hand G, to which Cord at G hangs the Weight R, which 
u muft be encreas'd by degrees, till the Excefs of the moving Power of 
" the Muicles D C becomes wholly infenfible, and they can fuftain no 
" more Weight than R, but be juft able to hold it with a Force brought 
a to be equal 5 then we may judge that the Momenta of the Powers of 
a the Mufcle, and of the Weight, are wholly equal, neither of thofe 



cc 



cc 



cc 



: and then the Tendon, mid the Mufcle DE is 

* either loofe and may be Separated from the 
J Limb and the Bones DAB;, or it is bound 
1 down to it by fome Ligament or Fa&ia as R ; 
g if the firft^ the Consequence will be as foU 
i lows : Becaufe the Bone A B cannot be turn' d 
4 up towards F G quite to the Situation A H, . 

* unlcfs it be drawn by the Contract ion of the muf 

* cular Cord DE, in which Cafe its Length 
& DE, in order to be fh or tend to DM, muft 
*" become hfs thaw the eighth Part of DE, 
6 which flyortening in the Arm will be of above 
6 a Foot and an half; this will not only be 

* troubhfome , but even impojjible. It would 

* be troublefome f becaufe the Breadth and 
*■ Thicknef s of the Arm would be vaftly encreas*d 

* to take in the JDimenftons G M equal to C E; 
*" fo that the Arm would upon this account on- 

* ly become as big as the Belly of the Animal \ 
* J which monftrous Thicknef s would hinder the 

* reft of the Motions of the Arm and of the 
L Animal ; then becaufe the Structure of a 
** Mufcle is-- fuch that it can be contracted but 
A a little^ feldom above two or three Fingers 

* Breadth : fuch a faftening of ths. Mufcle^ 



1 which' requires fo prodigious* a Contraction 
1 {namely of above a Foot and a half) would 
1 be altogether impojjible. But the Abfurdity 
' of fuch aVofitionwill m$ft evidently appe.ar\ 
1 if we fuppofe the Bone AB /fl be the Hu=* 
( merus {or upper Bone) of the left Arm, which. 
i is to be mov d ' every Way round the Joynt of 
4 the Shoulder fuppos'd at<D; that it may be 
4 brought to the Brcaft^ it is plain that it 
4 muft be drawn by the Mufcle ED fix 9 d to 
4 D the right Side of the Breaft\ another 
4 Mufcle to raife it up muft be fix*d on the 
4 top of the Head, and the Mufcle to bring it 
4 down muft have its Origin in the lower Fart 
4 of the Belly ; which Mufcle s r together with 
4 thofe of the right Arm, require a vaft 
4 fweJTd Space like a. great Tun; and' the 
4 fame would berequifd for the Mufcle s of 
c the Feet, which v?ould make a Man Jo far 
4 from being well joynted and clean, limb % d ; 
4 that he would be a ridiculous unwetldy Mafs 9 
*; unfit for Motion, and handling of Bodies^ 
4 Therefore fuch a Shape, was. entirely to be re-- 



Forces- 



4€ Forces overcoming the other. Now Experience Ihews us, that in a ro- Annotat. 
a bull young Man the Weight R does not exceed 26 Pounds, to which Le£L-JIX. 
; a mult be added the whole Weight of the Cubit and the Hand, which ^^\^sj> 
<c are nearly equal to 4 Pounds, and this Weight afts, not in the End of 
™ the Leaver as at B, but in the intermediate Place H, namely where 
<c its Center of Gravity is j therefore if another Weight of 2 Pounds be 
fufpended at B, which has the fame Proportion to the Weight of the 
€C whole Cubit as the Diftance OH to OB, we fhall have for our Lea- 
u ver an indivisible Lin£ and without Weight, at whole End B are fuf- 
u pended two Weights, namely R and the Weight of the Cubit, that is 
" in all 28 Pounds *, and then becaufe the Dire&ion CD of the Tendon 
"of the Mufcle that draws makes a very acute Angle with the Line 
" CO, becaufe the Tendon of the Mufcle exa&ly touches the Head of 
" the Joynt A, we muft from the fix'd Point or Fulcrum O draw the 
" right Line OI, perpendicular to C I the Dire&ion of the Tendon, and 
xc then from the Principles above demonstrated it will appear, that the 
cc Power drawing the Mufcle D C : has the fame Proportion to the Refif- 
a iance- of the Weight R together with the additional Weight above mentio- 
cc ned as the Diftance OB \ has to the Diftance IO ; but by a ftri£t 
" Examination it appears that O B the Length of the Cubit and Hand 
" is more than twenty times greater than the Semidiameter of I O the 
" Head of the Bone. Therefore the Strength and Power drawing the 
" Mufcle DC is above twenty times greater than the Weight R and the 
" additional Weighty and fince the 2 Weights are equivalent to 28 Pounds, 
" therefore the apparent Force with which the Mufcle draws the Cubit 
" and endeavours to bend the Elbow, is greater than the Force of 560 
" Pounds. 



■"' Proposition XXIII. 

" To find I the Force which the faid Mufcles exert, when the Humerus or 
u upper Part of the Arm is perpendicular to the Horizon, and the Cubit is 
" parallel to the Horizon. Plate 15. Fig. 5. PI. 15. F. 5; 

" Secondly, Let E A be the Humerus, and AB the Cubit making 
" a right Angle with each other, the Humerus being perpendicular and 
" the Cubit ftill horizontal: In that Pofition the Length of the Lea- 
" ver OB ftill remains the fame, and now at its End B is iuftain'd the 
" great Weight of 3 3 Pounds (as appears by making the Experiment) by 
" the fame Mufcles DC ^ but becaufe the Angle ICO made by the Ten- 
" don with the Bone OC is lefs acute than in the foregoing horizontal 
" Situation of the fame two Bones, becaufe when the Humerus E A is bent 
" towards the Cubit AB, the Tendon of the Mufcle DC adhering to 
" the Humerus is alfo bent yet the Angle I CO does not become a right 
" one, becaufe the Tendon at I is firmly bound with membranous Fafcite 
" and the outward Skin, which Ligaments ferve as a Pulley to keep the 

X % " Tendon 







cc 
cc 
cc 



At^tstt. cc Tendon towards A the Angle of the J§yrit 5 but yet the Tendon IC 
cc is not lb cloiely bound down at I but ttat it riles at little* and there- 
" fore the right Line O I perpendicular to the l>ire£lidn of the Tendon 
" CI becomes fenfibly longer than ift the foregoing Cafe, M We may 
" find by feeling our Arm and therefore the Diftance OB will bear a 
a left Proportion to 10, than it was found to do in the former Si- 
tuation Y but Whatever Proportion the laid Diftanees have, the 
&m reciprocally will the Fcfrci eontmaing the Mufele DC, and 
■ <c drawing the Bone^ have to tte Reliftande of the Weight R and 
the Weight of the Cubit together : Therefore that Force Will bear a 
lefs Proportion to this RefiftMci* than 20 to 1 } and if it appeared by 
the foregoing Enquiry th&t the gre&teft Ffrree of the Biceps and Bra- 
chitus MtllSleS was equal tor the Force 6f 560 Pounds j it Will appear 
" from the prefent Enquiry^ in which the greM- Weight R is of 33 
" Pdiittds, and, taking in the Weight of the Cubit , equal ffi 3 5 Pounds, 
" that the Diftance OI is only a tixteenth Part of the Diftance OB, and 
u not, as before^ a twentieth Part of it $ and therefore that the Diftance 
a IO being leafibly enete&s'd, there muft of eonleduence be /raised a 
" freatef Weight now* namely 3 5 Pounds, by thofe Mulcles. 

tm Ke?e we ftiuft take notic^ that thd' by reafon bf the bending of 
" the Lirtib E A B the Mufcl^ are not ftretclied as before, but muft be 
ifij fffiM rnMfnre rete'd j yet the moving Fdrce of each Mufcle has 
ct 2k'Ufs Power of contrallinf, bieaufe really the Muftles DC are not 
u bbt'fi fix'd to the Top bf the Humerus, but the Biceps is faften'd to the 
4 * iiaptila or Shdiilder-bone M'LE at L, but the Btachietis to the middle 
cc of the Humerus 5 and bi££ull the Scapula HEL> is always in the lame 
6C and tranfverfe Situation, the Humerus E A revolving about the Center 
u E of its Articulation, muft make the Angle LEO with the Scapula 
u the lefs acute the more the Humerus is bent downwards, and then the 
<c Origin of the Biceps Mufcle t) is ifibre rais'd and recedes farther from 
" the top of E the Head of the Bone, becaufe the Length of the Line 
* LDrfubtfehdihg the Angfe LEO is encreasM, and therefore the fore- 
w laid JVfulcie is Co itiuth the IMiore ftfeteh^d as the HuMerus is bent down- 
cc wards: Therefore tho' by reMBn of the Angle FOB the athlete 
u Mulcle be relaxed 5 yet the Biceps may be fb much the more ftretch'd 
by feafoh of the Ele^tibft of the Pbiftt D above the Head of the 



a 
it 



u P & O P O S I T I 6 K XXIV. 

Hence pPobaffiy fnay bt JtngJy found the apparent abfolute Forces bf ihe Bi- 
u ceps MdfcU) ibhieh is ^itiiteni to 300 Pounds, and of iM Brachieus, Which 
1. 15, V.6, " is tqUiJ to the Ftfree of 260 Pounds. . Plate 15. Fig. 6. 

€t Let ffie HuBeYUs O E be bent backward in order to ihake the Angle 
c * HEO is ^ute^s miiy b% aM likewile let the Cubit AB be kifie&ed fo 

as 



A Cmrfe of Experiment alPhilofophy. 157 

as to become parallel to the upper Line of the ScapuU H L, and then Amnofrat. 
" the alternate acute Angles HDI and CID will be equal to one another, Led III. 
" and then, as much as the Biceps, Mufcle DIC is relaxed on account of ^sT\j 
** the Acueefcefs of the concave Angle COE, juft fo much is it drawn and 
" ftreteh'd on account of the convex i\ngle HDO j therefore the natural 
u Tenfion of the Biceps Mufcle is in no wile alter'd, and remains exactly 
u of the fame Length as it had in the horizontal Situation of the whole 
u Arm ^ and as it fuffers no Relaxation, it will have the fame Force of 
€t contraaing itfelf as it exerted the horizontal Pofition. But the Brachieus 
' " Mufcle has not the fame Advantage, its Origin being in the middle of the 
" Humerus at F, and its End or Infertion at I near the Head of the Cu- 
u bit; aild becaufe the Angle EOCis acute, therefore the Brachieus Muf- 
" cle muft fuffer the greateft Relaxation, and therefore exert little or no mo- 
u tive Force : In this Cafe therefore one may find the moving Force of the 
« Biceps alone * (that is, if the Diftance O I from the Tendon to the Center 
« of the Head of the Cubit be not varied.) Let us fuppofe the Weight 
a R fuftain'd in that Situation together with the Weight of the Cubit to be 
" equal to 25 Pounds, and becaufe the Diftance IO is almoft a twelfth Part 
" of the Radius and the Hand BO, therefore the abfolute Force of the 
" Biceps Mufcle will be twelve times greater than the appended Weight R 
" together with the Weight of the Cubit , that is* it will be equal to the 
" Force of 300 Pounds, when the Brachieus exerts no Force by realbn of 
u its very great Relaxations then becaufe the joint Forces of the two Muf- 
a cles, the Biceps and the Brachieus^ working together in the firft Experi- 
" ment, were equal to the Force of 560 Pounds *, if from that Force we 

fubt raft: the moving Force of the Biceps alone, juft found to be of 300 
" Pounds, the remaining Force of 260 Pounds will be that which was ex- 
" erted by the Brachieus Mufcle, and that was the Thing to be enquired 
i€ into. 

"Prop o s i t r o n XXV. 

" fo find what Force the fame Mufcle s exert wkm the Cubit hangs down- 
a wards 9 whilft the Humerus is kept perpendicidar to the Horizon. Plate 15* PL 15. F. 7* 
" Fig. 7. 

" Now let the Humerus E A, and the Cubit A B be in one direft Line 

* and perpendicular to the Horizon 3 then the greateft Weight to be 
u fufpended at B, might be almoft immenfe, if the Strength and Tenacity 
w of the Ligaments could always refift and was wtetly infuperable. 

" If afterwards the Cubit be a little inflefted, fo as to make an obtufe 
" Angle EAB with the Humerus which is now perpendicular to the Hori- 
a zon, and an acute Angle BAK, with the horizontal Line OK, then 
a indeed may the great Weight R be yery much encreas'd/ becaufe if 
'« from B the Line BK be drawn perpendicular to the horizontal Line 

* A&, then the Weight R drawing the Leaver A B obliquely, afis in 

a the 



158 A Courje of Experimental Philofophy. 

Annotat. €c the fame manner as if it had been fufpended in the Point K of the 
Left. III. " Leaver OK ; and therefore we have now a new Leaver OK.fhofter 

w~"v~n/ " than OB ^ but the Force of the Mufcle railing the Leaver draws from 
cf the Point I having 10 for the Diftance of its Line of Dire&ion and 
cc confequently the abfolute Power that -contracts the Mufcle (which is al- 
cc ways the fame) has the lame Proportion to the Refiftance of the Weight 
cc -.R, as KO has to 10 y therefore if K O be only the double of O I, 
cc the Weight R which is fuftain'd in that Pofition will be half .of the 
" whole abfolute moving Force 5 and therefore equal to 250 Pounds \ and 
" if the Diftance OK be left than 01, then alio will the Weight R be- 
" greater than the moving Force of thofe Mufcles. 

" Hence may be gathered, that in the Flexion, or Elevation of the-'C«- 
a bit, the Effect of the lame Force which draws the Mufcle is continu- 
a ally diminilh'd- becaufe the Length of the Leaver OK is fucceffivcly 
€C encreas'd, and therefore the Weight R irrnil be decreased in the lame 
" manner. 



" P r o p o s 1 t 1 o n- XXVI. 

cc jFo find the Forte of the fame Mufcles when the Arm is placed in a fu- 
Pl. 15. F. S. cc pine horizontal Situation. Plate 15. Fig. 8. 

cc The Force of the Mufcles .bending the Cubit may be exerted in an- 
<c other manner, namely when the Cubit AB being in a fupine horizontal 
a Situation rauft be infle&ed downwards towards G by the Mufcles DC 
" which are now below the Cubit j for the Cord BLG being thrown 
" over the Pulley or Wheel ML moveable about a fix'd Axis M,, it is 
cc evident that whilft the Hand B defcends, the Weight R is rais'd, AB 
ic being then the Leaver whofe Fulcrum is (), and the Weight Re draws 
cc the End B of the Leaver upwards towards L, and the Power of the 
" Mufcles DC draws down the Leaver AB from I towards D 5 and 
€C therefpre thole Things which have been faid before will alfo be veri- 
" fied here, only with this Difference, that in the former Cafe the End 
u B was drawn downwards, not only by the Refiftance of the Weight R > 
" but alfo the Weight of the whole Cubit and Hand \ but on the con- 
a trary, here the Weight of the Cubit does not aft counter to, but helps 
" the Power of the Mufcles to draw} becaufe, that as in this Situation 
a the Mufcles draw down the Cubit, ib the Cubit alfo a£ts downwards by 
a its Gravity, and thefc two Powers taken together have a Momentum e- 
a qual to that of the Weight R -j and as in the firft Cafe the Weight of 
cc the Cubit- was added to the Refiftance of the heavy Body R, now it is 
" added to the Power of the Mufcles } and becaufe the greateft Power 
* By the 22d" of the Mufcles D C was Ihewn to be equal to the Power of 560 Pounds*, 
Prop, above " therefore if the Leaver A B was of no Weight, when the Diftance O B 
cited. a i s jfbund to be twenty times th*e Diftance OI, the Weight R ought to 
a be of 28 Pounds J but becaufe the 2 Pounds added to R are in Mqui- 

€C Vibrio' 



A Courfe of Experimental PhiJoJbphy, 1 59 



a Vibrio with the Weight of the Cubit AB (that is, as they render it a Amiotat 
Beaver without Weight) therefore the Weight with its Adjunct making Le£t HIT 
u up 30 Pounds will be the greateft Weight that can be fuftain'd by the KS~Y*\J, 
H Force of the Mufcles in that Situation. 

a This may be fhewn another Way, becaufe the defcending Weight of 
u the Cubii being as 2 Pounds hanging at B, is made to afl: equally with 
€C a drawing Force of 40 Pounds applied at I (by reafon of the reciprocal 
a twenty fold Proportion) and the proper Force DC I will be of 560 
u Pounds - 9 therefore this Force, together with the Momentum of the Cu- 
c « bit afting with it, will produce an Effefl: equal to the whole Weight of 
4C 600 Pounds. 

But what appears moft wonderful is the Force of the Mufcles that 
move the lower Jaw, which the laid Borelli confiders in the 87th and 88th 
Propofition of the firft Part of his Book abovemention'd, where he fhews 
that thofe final! Mufcles, all which taken together do not in a Man exceed 
the Weight of one Pound, do yet exert a Force equal to 534 Pounds 
and in Maftif Dogs, Wolves, Bears and Lions, have a Force vaftly fiipe- 
rior, to enable them to break large Bones as they do daily in their 
Feeding. 

7. [3 5. • — — And if the Arm CW he fet freight in a Line with VQ^ 
Sec — the Inf rument will plainly appear to be a Leaver of the fir f Kind. 
Tho' the bended Leaver is not an Inftrument of common Uft, except in 
the Hammer and Tools of that Kind, yet the Consideration of it is very 
neceffary in rhe Explanation of feveral Machines' that virtually contain fitch 
a Leaver - 0 efpecially in ftatical Proppfitions, of which we will here give 
fome Examples. The Cafes ; of the Inclin'd Plane and the Wedge * may * 4 8 > 49> 5°i> 
he clearly folv'd this Way. As for example, when the Weight P 1 pi 5 ^ p 
tains the Weight ■ W upon the incliri'd Plane A B drawing the Center of 
the Weight in the Line MW parallel to the Plane, one may confider in 
the faid Weight the bended Leaver ;W T n whoie longeft Brachium is W T 
and the fhorteft T h. Nbw, as the Line, of Direction of the Power is 
M W parallel to the Plane, TW a£i:ed upon at right Angles muft be the 
Diftance of the Power - 0 and as W n is the Line of Direction of the Weight, 
»'T at right Angles with it muft be the Diftance of the Weight } confe« 
quently as »T. (the fioott Arm of the bended Leaver) : is ft? W T (its long 
Arm) :: fo is the Power ¥ \ to the Weight W. Now,, as the ffiiangles 
W T n a?id ABC are ftmilar^ the Power thus confder r d : is to the Weight . : : 
as B C the Height of the Plane : to its Length A B 5 Which" was prov'd in 
its.Place # . But if the Power had drawn the Weight in a Line parallel* A9> 
to the .Bale of the Plane, "which is- the- Cafe «6f the-: Wedge^ its Effefl: might 
be thus explained. As the Power a£b obliquely at the End of tlie long 
Brachium of the bended Leaver W T'fc," its acting Diftance muft be found 
by drawing from the Center of Motion T, T <r perpendicular to the Line 
of Direftion of, the... Power a . which as the long 

, Brachium^ 



i6o ji Ourfi ^ E^per 

Annotat. Brachium of the Leaver, whilft nT ftill is the fliort Arm and a#ed ufo® 
Left. Ill by the Weight at right Angles. Therefore the Qii^tity or <rf 
u>^V*\> the Power m will now be found by this Analqgy, viz*. 

As the long Arm of the Leaver, now T o ; 

Is to tke floort Arm Tm ; : 
$v is W the height : 

Sft R'the Power 3 #r Bafe K Q : to the Height CB. 

* 48, 49,50, When 1 confider'd the IncMi Plane as a mzchmml Organ % J only 
$i, 5 2 ' took notice of two Applications of the Power, the one with its Line of 

Direction parallel to the Plane, and the other (which reduc'd it to the 
Wedge) with its Line of Direffion parallel to the Bafe of the Triable, 
that is, inclin'd to the Plane as much as -the Plane is indki'd to the Bpj> 
zon, the Angle WBA (calPd the Aqgte of fraction ) being equal to tlm 
Angle B AC, becaufe of the Parallels WB, AC; but m m eomgomd 
Bt|gme« # and in the Ufe of Carriages the Angle of Tra£Han or Incline 
tion of the line rif Direction of the Power to the Plane is yfry yaria^ 
ble, we give this Way of confidering a bended Leaver in the Body to fee 
drawn up for the Solution of all Cafes, which will appear by the £oMmn$ 
Example. 

JLet DLB be the Angle of Tra&io% as when the Power n draws over 
the Pulley pin the Line pL. WT> is a beaded Leaver whole Center 
of Motion is- T the Point where the Ball W touches the Plane, nT the 
ihort Arm of the Leaver on whofe Extremity n may be coauder'd the 
Weight as %ported and prolong at right Angles, beeaufe its Line of JDi- 

* L.z. 45. ration .goes through n % and W T the iomg Arm of the Leaver to which 

the Rower k apply 'd obliquely. But as Tz perpendicular to the Line 
of DireSion of the Power is its aSling Difiance> we may eonjfider Tz 
>as the long Arm of the Leaver. Then the whole Cafe will he folfd 
hy ilils Analogy, viz. 

Ms the tmg Arm of the Leaver \ now z T ::: 

Is to the Jhort Arm Tn : : 
■•$0 is the Weight ; 

So u the Power. 

$mm one may find this Mi bended Leaver,, in any Dire&jon of the 
"Powei;, chat is, in any Angle of Tra&ion, this jeneral Rule % all Dir^s- 
ti©ps of the Power may be deduced from it. 

Me i&ngk of Tmfkion is ifoeifagk the I hroet > draws in a Line of Mirifcionfa* 
mhith ihe Line of DiretHion of the "timer raUel to tke0me, thm 'Mtl-Jte m .J^lc <if 
wahs y>kb -the ?.hns i ; mii' c^fe^tienffy. vihen. SraSiQ^ 

As 



A Courfeof Experimental Philofophy. 161 



As the Sine of the Angle of Inclination of the Plane : 

To the Sine Complement of the Angle of TraElion :: 
So is the Power ; 

To the Weight. 

But to prove how the Rule is deduced from the bended Leaver, wePIio. F. 14. 
muft fliew that #T, the fiiort Arm of the faid Leaver, is always to its 
long Arm zT ? as the Sine of Inclination, to the Sine Complement of the 
Angle of Tra&ion 3 or that CB in the Triangle ABC : is to Lz in 
the Triangle Thz :: as nT : is to Tz , and then we fhall draw ibme 
ufeful Corollaries from our general Rule. 

Demon s.tration. 

Since WT is perpendicular to AB, and the Angles W^T and AqE 
equal (becaufe they are vertical Angles, the Triangle AqE (reflangular 
at E) having two Angles equal to two Angles in the Triangle W^T, 
the third Angle A muft be equal to the third Angle ?WT, confequently 
the Triangles will be equiangular, and therefore fimilar (by 4. 6. EucK) 
and as is the Sine of Inclination for the Radius Aq (becaufe in its fi- 
milar BC is the Sine of Inclination for the Radius AB) fo alfo will qT 
be the Sine of Inclination for the Radius W q. But as T n which is pa- 
rallel to the Horizon falls upon W q, which being the Line of Direction . 
of the Weight, is perpendicular to it, the Triangle WT^ is fimilar to 
WqT (by 8. 6. Eucl) and thus Tn the fliort Arm of our bended Leaver 
becomes the Sine of Inclination for the Radius WT : Which was one of 
the Things to be demonjlrated. 

Further, as T z is by Conftruaion perpendicular to L W, the Triangle 
W%T is fimilar to LWT (by 8. 6. Eucl) therefore the Angle zTW 
is equal to WLT the Angle of Traction} fo that as LT is the Sine 
Complement of the Angle of Traction for the Radius L W, T Z (che long 
Arm of our bended Leaver) muft be the Sine Complement of the Angle 
of Traftion for the Radius T W. Which was the other Thing to be demon- 
jirated. 

COROLLARY I. 

Here follows, that when the Line of Direabn is parallel to the Plane, 
the Power is the lead that can be for that Inclination of the Plane, be- 
caufe then the Sine Complement of the Angle of Traftion is changed into 
the Radius or Whole Sine, that is, TZ becomes T W, or the long Arm 
of the Leaver W T being afted upon at right Angles expreiles the aaing 
Diftance of the Power • or, ftriftly Ipeaking, the Angle of Traftion va- 
nishes. But if the Power ihould draw direftly up in the Line W*, it 

Y muft 



Annotat. 
Left III. 



1 62 A Courje Experiments Phtiofophy. 

Annotat. mud be equal to the Weight* becaufe then W#T being the Angle of 
JLe£t. III.Traftion, its Sine Complement (q W being Radius) would be # T, which is 
VTV^O equal to the Sine of Inclination here exprefs'd by the laid Line. Hence 
it is plain, that if an Horle draws a Burthen up Hill by means of a Cart 
PI. 10. F. 14. or any rolling Machine, he will draw it with fo much, the more Eafe, as 
the Line of Direction by which he draws the Load conies nearer to a pa- 
rallel to the Slope of the Mountain along which he draws. 

C O R O L L A R T II. 

It follows alfo, that if the Line of Direction, as B W and w W paral- 
lel to AB, make the Angle w W B equal to the Angle w WD, the 
Power applied at B will be equal to the Power applied at D 5 becaufe in 
fuch a Cafe the Angles of Traftion WLB, WBL will be equal, fince by 
29.1. EucL the Angle W L B is equal to its external oppofite D W w, which 
is fuppos'd equal to the Angle w WB, and confequently to its alternate 
W B L. Whence it follows, that if the Line of Bire&ion of the Power^ 
as Wa, and the Line WT perpendicular to AB, make the Angle TWa 
equal to the Angle of Inclination A (or fWT) the Power applied at a 
will be equal to the Weight by Cor. 1. becaufe then the Angle of Trac- 
tion W a L is equal to the Complement of the Angle of Inclination A % 
that is, W^L is equal to W qa = ABC. 

COROLLdRT III. 

Latlly, it follows alfo^ that if the Line of Direction of the , Power be 
W T at right Angles to the inclined Plane AB, which makes the Angle 
of Tra&ion a Right \ the Power applied at T or in any part of the Line 
tT muftbe infinite. That is as much as to lay, that a Power that fliould 
draw the Weight D directly from the Plane, or direftly againft it, would 
not keep it there, let its Intenfity or Force be ever fo great, becaufe in 
that Cafe the Sine of the Complement of the Angle of Trafticn- . is redu- 
ced to nothing, or being infinitely finally the Power applied at T rnuft be 
infinitely great j fince, by what we have fhewn, that Power : muft be to 
the Weight :: as the Sine of the Angle of Inclination : is to the Sine Com- 
plement of the Angle of Tra&ion. 
* 28,35,45. Before I quit this Subject of Bodies fupported or drawn on inclin'd 
Planes, I beg leave to apply what has been laid in the lecond Lefture 
to fhew generally why a Body will be fiiftain'd on an inclin'd Plane by an- 
other Body of lefs Weight (if the former be drawn in a Line of Direc- 
tion parallel to the Plane, and the latter hangs perpendicularly) when the 
Weight of the great Body : is to the Weight of the little one :: as the 
Length of the Plane : is to its Height* The whole is deduced from this. 
Principle laid down and explained in the lecond L efture, viz. That if the 
Center of Gravity of a Syjiem of Bodies does not defcend % the Bodies cannot 
defcend* 

Now 



A Courfe of Experimental PMlo/bphy. 1 63 

Now to apply this to our Purpofe. ADB # is an inclined Plane, whole Annotate 
Height is D B. If by means of a Pulley P the Weight w hanging perpen-Le^ III. 
dicularly does by a String hold the Weight W on the inclin'd Plane, and thole <>VNJ 
Weights are to one another, as the Length of the Plane to its Height^^-^ F.p- 
(which here is as 2 to 1) they will remain at Reft (that is, keep each 
other in Mquilibrio) whatever Part of the Plane W is laid on. Firft, let 
the Situation of the Bodies be W and w } draw the Line mn which 
joyns their Centers of Gravity, and having found their common Center of 
Gravity at C* (fin = 2 Cm) draw H h an horizontal Line through that* By L. 2. 
common Center t, and then whatever Pofition the Bodies are in, or what- No 37. 
ever Part of the Plane W be placed on, their common Center of Gravity 
will ftill be in the horizontal Line Hb : If W be remov'd to V, w will 
fall to u, and the common Center of Gravity will be at k : If the Centers 
of the Bodies be at E and e> their common Center of Gravity will be at 
K, ftill in the fame Line Hh 7 which may be eafily prov'd, becaufe the 
Triangles nhC, m¥LQ^hqk y rok, &V. are all limilar. Since therefore 
there is no Pofition of W on the Plane and of w in the Perpendicular wq 
which can alter the Height of the common Center of Gravity of the Bodies 
they mufi be in Mquilibrio, becaufe they can't fall unlefs their Center of 
Gravity defcend. E. D. 

COROLLARY. 

Hence alfo appears the Reafon why two unequal Bodies will fuftain 
each other upon unequal Planes of the fame Height, whofe Lengths are 
to one another reciprocally as the Bodies. For example, let the Weights 
F and G*, join'd by the Cord FPG running over the Pulley P, be to*Pl,x 5 .F.io 
one another in Weight as the Planes A B, B D (whofe common Height 
is BE) on which they refpeftively reft. Find their common Center of 
Gravity C, and through C draw an horizontal Line y then you will find 
as before, that however you alter their Situations on their refpeaive Planes, 
their common Center of Gravity will ftill be found in the fame horizontal 
Line that goes through C, &c. 

8. [37.——-^ upper or Jix'd Pulley adds m Force to the Power, but 
mly prevents the Friffion by making the Rope- run eafily; and fo much the 
more as the Sheever is bigger than the Center-Pin upon which it turns ^ How 
much the Friftion of a Roller or upper Pulley is diminifh'd in proportion 
as the Center-Pin, or the Gudgeons are lefs in Diameter than the Wheel or 
Roller I Hiall exaftly fliew in the next Lefture, Now I lhall take notice 
of the Diminution of Preffure upon the Center-Pin of a Pulley which al- 
ways happens in a certain Proportion of the Weights which hang on each 
fide, when they are in Motion, and that without Regard to the Bignefs of 
the Pin, which in this Cafe may be confider' d as a Line. The Thing 
in general is comprehended in the following 



Propo 



1 64 A Courfe of Experimental Philofophy, 

Annotat. 
Lea III. 

{y^sj Fro POSITION. 

When a String or Rope runs over a Jingle Puiky or Roller by the x Defcent 
of the preponderating Weight (the other Weight rifing at the fame time) the 
Preffure on the Axis of the Pulley is always equal to the Quadruple of the 
Produft of the Weights multiplied into one another) and divided by the Sum 
of the fame Weights. 

PL 55. F. 11. Tlate 15. Figure 11. 

The Pulley is DE its Center C, the Weights^ and ^ and the running 
RopepDrE^. I lay, that the Prefllire on the Axis or Center C is — 

4 P ? 
p 4- q. 

H.15.F.12. Tkte 15. Fig. 12. 

The Pulley being reprelented in this Figure by the fame Letters as 
before, draw at pleaflire the Lines D d and Ee in which the Weights rile 
or fall. Draw from the Center of the Pulley Ck parallel to the faid Lines ; 
then thro' the Point 0 taken any where in the Line Ck draw the horizon- 
tal Line pq and taking the Diftance pV equal to #QL draw the oblique 
Line FoQ^ From the Point c the common Center of Gravity of the 
Weights reprefented by the Letters p 7 q, and fuppos'd to hang at thofe 
Points, let fall the Perpendicular eg till it meets the Line PQ. If we 
confider pq as a Balance of unequal Brachia whole Lengths are in the re- 
ciprocal Ratio of q to p, fo that the Weights p and q fhall upon it keep 
one another in Mquilibrio, we may call c q the Leaver of the greater Weight 
q^ and pc the Leaver of the lefler Weight p •> and if w r e fuppofe the 
Weight q to delcend as far as Q_whilft the Weight p rifes as far as P 
(through an equal Space) becaufe Fg is to g Q_ as p c to c q> the Line 
eg will reprefent the Defcent of the common Center of Gravity of the two 
Weights. 

De monst r a tion. 

The Sum of the Weights p-\- q : is to their Difference q — p : : as 
the fum of their Leavers pc »\- cq : to their Difference pc — cq : and 
confequently : : as half the Sum of their Leavers oq : to half their Diffe- 
rence - 9 and like wife by 2 and 4. 6. Eucl) : : as qQ_ the Velocity of 
the Weight defending : to eg the Velocity of the Center of Gravity de- 
fending. Now taking out of q a Weight equal to p 7 there remains only 



A Courfe of Experimental Phihfophy. 1 65 

q p to give Motion to the Weights by the natural Gravitation of it. Annotat. 
But the Momentum ofq — p by the natural Gravitation is q v — p v (v be- Left. IIL 
ing taken for the natural Velocity of the Weight falling) therefore the Ve- 

Cj v — - p V 

locity exprefs'd by ^Q^will be r^^i kut before, we had this Ana- 

q 4- p * 

logy p Af q : q — p qQ_- cgh therefore we have p -\- q : q — p : : 

q «u pv 

— — -j— * £g the Velocity of the Center of Gravity, which will be 



Therefore the Momentum of the two Bodies will be that Velocity mul- 
tiplied by the two Bodies, and confequently the Momentum of the Fall 

of the two Bodies will be f— 2 t>f \- p x X v : Now if the two Bodies 

2 \ P 

f -\-/> fell wholly, their Momentum would be qv -\- pv; but as we niuft 

fubtraa only that which falls of the Bodies, viz. ^ 2p ^' p% * v , there 

q-vp 

is a Remainder of the Bodies which does not fall, and that Remainder of 
confequence muff reft upon the Center and prefs the Axis. Now this Re- 
mainder, by making the Subtra&ion, appears to be - 4 f^ . jS>. E. B, 

p - q ^ 

Scholium. 

Hence it follows, that if p be equal to q (in which Cafe there will be 
no Motion of the Weights, the Preffure will be ip = p q j and if f be 
infinite, the Preffure is ^p. 

To try. this pra£Hcaliy, I . made the following , 

Exp e r i m e r t. TV. 1 5. Fig. 13. P j t I5 .f. 13 

I fcrew'd a very nice Pulley D to the bottom of the Scale h of the 
Balance AB moveable round the Center C, and having balanc d the Pul- 
ley by Weights in the Scale I faften'd to a String the two Weights p 
and £ weighing 2 and 6 Ounces } then having put the String over the Pul- 
ley D, I plac'd 6 Ounces, and one Penny Height in the Scales kept from 
riling by a Thread, which join ? d in bottom to the fix'd Hook H, whilft 
the whole Balance hung by another fix d Hook at M Supporting the 
great Weight q by a Ruler held at e horizontally under it, I-.orr the 
flidden. remov'd e to give, q, leave to defcend which when it did, the 
Preffure on the Axis of the.. Pulley D was fo much diminifh'd (during the 

Rile 



I 




Philojbphy. 



Annotate Rife of p and Deleent of q) that the Balance a funk by the AfHon of the 
Lett. III. little Weight d 0 even when it was a great deal lefs than a Penny Weight, 
VW as plainly appeared by the Thread Ma growing flack. 

When q was = 12 Ounces and p = 3, the Counterpoife in the oppofite 
Scale was 9 Ounces and 12 Penny Weight according to the Theory, and 
the Experiment agreed with it, there being a vifible Defcent of the Scale 
^, by the Addition of the little Weight d, even when it was lefs than the 
300th Part of q, &c. Take q and p in any other Proportion, and ftill the 
Experiments will agree with the Theory. 

This JVay of confidering the PreJJure upon the Axis may alfo be applied to 
the Axle in the Wheel in the following manner. 
*Pl.ij.F.i4. Let A C B * be an Axis in Peritrochio, whole Wheel is AB, C the 
Center or Axis of - Motion and AX the Axle, q one Weight (commonly 
the greater Weight) and p the other, the Line qp 7 as a Leaver unequally 
divided at 0, repreftnts by its Part qo the Arm or Semidiameter of the 
Axle A C, and by its Part op the Arm or Semidiameter of the Wheel C B„ 
The Bodies p> q, being in the Situation reprefented in the Figure, and 
pb greater than qa, the Part of p which makes an /Equilibrium with q 

Will be and coniequently there will be left of p only p ~ ^~ or 

^ * (making V equal to the Velocity with which Bodies fall) 

to give Motion to the two Bodies becaufe the Remainder of the Weight 

q b V -4- q a V 

of the two Bodies, p V \ q V, namely — — -j of the two Bodies of 

/Equilibrium q 4- will remain preffing on the Axis of the Machine. Let 

a u 

u be the Velocity of />, the Velocity of q will be — , and its Momentum 

will be which added to pu the Momentum of p gives tljL^^A^Jf 

equal to the whole Momentum produced by the Force or Momentum 

— • Therefore lince the Momentum produced is always equal 

1 , ■ i.t 1 - r pbuA-qaV pbV~qaV 
to the Momentum which produces it, we have — — —~ = x —~ 1 — 

, . - . pbV — • qaV , au pbaV — qaaV 
which gives u = - — — . — - — and — = ,-7-, which 

pb 4- qa b pb b ~Y qa b 

gives the Momentum of q = — f f ~ - X V, which Momentum p 
■ pbb 4- qab 

will give it as it bears on the Axis, and confequently the Axis muftfuffer 

the Preffure of it, And as q 7 by its Reaction upon j>, will make it lole 

as 




A Courfe of Experimental PhU&Jbphy. i 

as much (bearing alfo upon the Axis) or will as much retard its Defcent, Annotat. 
the Axis rauft of necefiity by this equal Aftion and Reaction bear the Left. III. 

double Preffure **** * ~~ 2 ^ r aa X V ; to which adding the Weight 
p b b ~\- q a b ° 

tLjJJ? x V of the two Bodies of ^Equilibrium, the whole Preffure on 

the Axis will be equal to #*H-gggf f iphga — ggaa X V _ 

pb b -\- qab v 
viding by the Denominator as far as we can) it will be equal to q 

3 pbq a — ~q~qaa^%.\f 

~p~bb~-^Jab * J - herefore the Axis bears as much Weight as if 

it fuftain'd the Quantity of Matter q + if* 

2 r pbb -\- qab • 

C O R O L L A R Y I. 

If pb^= qa, the Preffiire is q -|- p } or q ~y it (according as pb is 



down for qd t or the' Reverie in the Form gl**+gg-**+3 P*sa—1ta* 

ppb\qab 

becaule in that Cafe — = p. 

b 

CO ROLL ART 11. 

If p be infinite, the Preffure is q _|- . or the Weight f together with 

three times the Weight that is able to keep it in Mquilibrio at the Di- 
ftance of p, as in the Pulley above mention'd, where the Preffure is 

Aqp 

fjftf If t be infini te, the Preffure then is 4 p $ and if b be infinite, the 
Preffure is only equal to q . 

N. B. may he given as a general Rule for the Preffure on the Axis 
either of a Pulley or of a Wheel and Axle^ by the two Bodies atting 
againfi each other ^ viz. 

As the Momentum of the two Bodies falling freely % 

To the Momentum which is loft when they aft on each other by means of 

the Machine : : 

So is the whole Weight of the Bodies i 
To the Weight pr effing upon the Axis* 



1 68 A Courfe of Experimental Philofophy. 



Annotat. 

Left. III. p. [41.—- While 2 goes down to a ? 1 goes up to Bjujl twice as far 7 Sec. 9 } 

w~V~s^ There is another Cafe of raifing a Weight by feparated Pulleys, which I 
omitted here. It is mentioned by Dr. Pemberton in his View of Sir Isaac 
N.ewtonV Philofophy. I fhall firft give his Solution of it, and then fhew 
how eafily it may be reduced to our Rules, by proving, that however 
that Cafe is varied, there will be ftill a reciprocal Proportion between the 

*Pl.TS.F.i 5 .Power and the Weight The Weight W * is fuftain'd by the Power P 
by means of the three Pulleys C, D, E, of which D is fix'd and the others 
moveable, and a Rope goes from the Weight to each Pulley as repre- 
fented in the Figure. cc To explain the Etie£i of Pulleys thus applied^ 

*Pl.i5.F.id.« ic will be proper to confider different Weights hanging as in Fig. 16*. 

" Here if the Power and Weights balance each other, the Power P is 
" equal to the Weight w the Weight W is equal to twice the Power P or 
cc twice the Weight w, and for the fame reafon the Weight W is equal to 
cc twice the Weight w, or equal to four times the Power P. It is evi- 
cc dent therefore, that all the three Weights w> w, W together, are equal 
cc to feven times the Power P. But if thefe three Weights were join'd 

tPl.i5.F.i5." in one, they would produce the Cafe of Fig. 15 f. So that in that Fi- 
cc gure the Weight W, where there are three Pulleys, is feven times the 
cc Power P. If there had been but two Pulleys, the Weight would have 
cc been three times the Power ^ and if there had been four Pulleys, the 
a Weight would have been fifteen times the Power. 

To explain this our Way, let us confider the Weight W to be rais'd 
one Inch, as from the horizontal Line AB to the horizontal Line ab 7 and 
from the Make of the Machine find what muft be the Velocity of the 
Power. Firft then, the Point F of the Rope going over the Pulley C, 
muft defcend one Inch, viz. from the Line ¥ f to Gg (becaufe W faf- 
ten'd to the faid Rope riles one Inch by Suppofidon) and the Pulley D 
faften'd to the faid Rope DF muft alfo deicend one Inch. From the 
Decent of the Pulley D one Inch the Point H of its Rope muft deicend 
two Inches, as it is fiipplied from both Sides of the Pulley \ but an Inch 
more of the faid Rope muft be fupplied by the Rife of the Weight W \ 
therefore the Point H will defcend three Inches, or from Hh to lu 
Laftly, as the Pulley E defcends three Inches becaufe it hangs by the 
Rope HI, the Point K of the Rope KP (being fupplied from both Sides 
of the Pulley E) muft defcend 6 Inches on that Account, and one Inch 
more on account of the Rife of W : Therefore the Point K of the laft 
Rope by which the Power P pulls, will defcend feven Inches, viz. from 
the Line Kk to the Line L/, whereby the Power alfo will deicend the 
fame Diftance, namely from P to p. Confequently one Pound at P in- 
ftead of the Hand will fuftain the Weight W feven times as big, 7 x 1 
being equal to 1X7. Therefore in this Combination of Pulleys? 'as well as 
in all other s y and indeed in all mechanical Engines [as we have often faid) 
where there is an ^Equilibrium, there will be a reciprocal Proportion between 
the Intenfities of the Power and Weight and their Velocities. 

10. Dfi«- — ~ 



A Cmrfe of Experimental PMlofophy. 1 69 

j/knnotat 

10. til'' the Ropes, Sec. (applied Co Pullies) are always fuppos'd ^-Left. IIL 

rallel, except where it is otherwise exprefs'd.J Tho' in a Combination of ^v\/ 
Pullies, where the Iaft Pulley is a fix'd one as in the 4 th, 5 th, 6th, 7th, 
8th and pth Figures of Plate 10*} the Force exerted (fuppofing a Man* P1 I0 F , 
or Men to draw) is the fame in whatever Direftion the Power draws the 5, 6, lt 's, 9. 
running Rope j yet if the Ropes that are applied to the' Block or Blocks 
which come up with the Weight, are not parallel, Force will be loft in 
Proportion to their Obliquity. 

Suppofe the Weight W * together with the lower of moveable PulIey * P i i S F.i 7s 
C, from whofe Center it hangs, to weigh 6 Pounds } if it was fulpended 
at c, it would require a Force equal to 6 Pounds to fupport it; and there- 
fore if you fuppofe two upper or fix'd Pullies as A, B, to have over 
them a Rope, at each End of which hangs a 3 Pound Weight, whilft the 
middle of the Rope comes under the Pulley C, it is evident that the two 
Weights (or rather Powers P and P, being both together equal to the 
Weight, muft alfo fupport and keep it in Mquilibrio. Now, fmce P and 
P balance one another, if P be taken away and the Rope be made faft at a, 
P alone will fupport the Weight W, as we have faid and explained al rea- 
dy-}-. And this will appear more evident, if we reduce the Pulley C tot 37- 
a Leaver after the manner ihewn in the fecond Note of this Ledlure*. In * L 3. Ann. 
this Cafe mn is a Leaver of the fecond Kind, in which the Center of Mo-*-P- 13** 
tion^or Fulcrum is at », the Weight W draws at right Angles at 0 with 
the Diftance 0 n, whilft the Power with the double Diftance fnn draws 
alfo at right Angles in the Direftion mB. Now, if the Pulley B be re- 
moved to b, the Direction of the Power will be changed and become b m, 
confequently its Force will be diminifli'd in proportion to the Obliquity 
of its Direaion ; that is, the Power able to fuftain the Weight in the 
Direction b m : is to the Power which foftains it in the Direaion m B : : 
as*» :.i8 toB«+. f tL. 3 .Ann.j; 

fcrom this Confideration may be deduced this general Rule for knowing P Hi, 142. 
the Intcnfity of the Power or Powers, which drawing obliquely over fix'd 
Pullies caule a Weight hanging from the Center of a moveable Pulley to 
rile directly up. 



As twice the tangent of the Angle of Inclination (that is, the Angle made 
by the Line of Direaion of the Power, which is the oblique Rope) 
with the Horizon : 
To the Secant of the faid Angle : : 
-So is the Weight, when one End of the Rope is fix'd : 
to the Power drawing obliquely. 

But if two Powers (one at each End of the Rope) be made life of, thtn 
the Analogy will ftand thus \ 

TL As 




170 A Courfe of 

AnnoTat. twice the tangent of the Angle of Inclination % 

Led. III. 21? twice the Secant of that Angle : ; 

L/"V"SJ So is the height : 

7*o the two Powers taken together. 

P R E P A R A T I O N. 

*Pl.i-.F.i7. ^et t ^ ie P u ^ es A,B,* be remov'd to a, b, and the Line bm and ao pro- 
)f duc'd till they meet at C join the Centers of the Pullies by the 

horizontal Line ab\ and from the Point E taken at pleafure in any Place 
of the oblique Rope draw ED parallel to ab 7 and making = DC 
draw EC: Draw or perpendicular to CB. 

Demonstration. 

Since cC is the Line of Dire&ion of the Weight W it muft be per- 
* 22. pendicular to ab # the horizontal Line, and confequently parallel to B m \ 
therefore the Triangle cCb is fimilar to the Triangle Bmb (by 4. 6.. EucL) 
and for the fame reafon DEC is fimilar to c bG, and ^DE is' alio fimi- 
lar to them and equal to DCE, becaufe of the right Angles at D, and. 
the common Side D E and equal Sides DC - Dr. Befides, the Triangle 
aCcis fimilar to the others abovementionM, becaufe as the Weight W 
(or its Center of Gravity) defcends as low as it can, aCb muft be an 
Ifofceles Triangle biffefted by the Line of-Dircftion cC. Now if Cc re- 
prefents the Intenfity of the Weight hanging on the Center of the lower 
Pulley C, its Half D C will reprefent the Intenfity of the Power drawing 
direftly or at right Angles to the Leaver m n^ and C E its Intenfity when 
drawing obliquely $ and fince the Afigle DEC = cbC 7 EC the Secant 
of D E C will be the Secant of the Angle of Inclination j and DC the 
Tangent of DE C will be the Tangent of the Angle of Inclination and 
its Double is Cc reprefenting the Intenfity of the Weight. Q. E. D. 

If the two Powers are us'd, P will draw with the fame Obliquity as P 
becaufe the Angle aCc^cCb, therefore P ^ P : p *\-/> : : DC 4- Dc : 
CE -\-Ec. $.E. D. 

The firft Analogy may alfo be demonftrated by the Dottr-ine of the 
Leaver - 9 for if we confider that bm is the Line of Direction of the Pow- 
er drawing the Leaver mn obliquely, or perpendicular to bC (that is bm 
*L. 3. . Ann. produced) will be its afling Diftance * ; and the Intenfity of the Power 
5-P- H 2 - afting at right Angles : will be to its Intenfity afting obliquely :: as nr : 
to nm } but becaufe of the right Angle nrm and the common Angle nmr y 
the Triangle n m r is fimilar to 0 C m and c C b \ and therefore n r will be 
the Tangent and nm the Secant of the Angle of Inclination. j£. E. D. 

This may be experimentally tried by taking the Weight W together 
with its Pulley equal to 6 Pounds, and the Weights P and P equal to 5 
Pounds each; for then if the Pullies A and B be fix'd at the Diftance 



A Com fe of Experimental Phihfophj. lyi 



of 8 Inches from each other at their Circumference, as at a and b y the Annotat 
three Weights will not reft till the Line Cc be juft 3 Inches long, in which Led. III. 
Cafe the Triangles a C c y cCb, EDC, D E c 9 moC, and mnr will have <S~\/^sJ. 
their three fides in the Proportion of 4, 3, and. 5. But the beft Method pl * *5- F - *7- 
of trying all Cafes of this Kind, is to make ufe of the Machine contrived 
by Dr. s^Gravefande for that Purpofe. (See his Introduction to Sir Ifaac 
Newton's Philofbphy, Part No. 20s.) On the Plank or horizontal Board 

are fixed two Standards S, S, which have, each on its upper Pare, afPI.15.FaS,' 
Sextant with feveral Lines drawn from a Center taken on the upper Part 
of a Pulley, along Which Lines going over the Pulleys may be ftretch'd. 
In the middle of the Lines are written the Numbers which exprefs the 
Secants of the Angles which thofe Lines make with the Horizon, and at 
the Ends of the Lines are written the Numbers exprefflng the Tangents 
of thole Angles. Now in making Experiments it will appear in every 
Cafe where there is an ^Equilibrium^ that the Weights Q_ and Q_ are as 
the Numbers in the middle of the Lines along which the Threads are 
ftretch'd and the Weight P as the Sum of the Numbers at the Ends of 
thofe two Lines. 

11. [48. — — A lefs Power nbill ferve &c. — unlefs it pujhes the Body 
ugainfi the Plane y &c. or draws it away from the Plane y &c] We have 
in the 7th Annotation confider'd all that relates to a Body moving on ah 
inclin'd Plane, and therefore refer to that} but it will not be improper 
here to take notice of the Difference between high Wheels and low ones, 
as they roll over uneven Grounds or Rubs : Becaufe tho' this Motion 
cannot be confider'd in every Refpefl: like the rolling of Bodies on in- 
clin'd Planes \ yet there are a great many Things alike in both Cafes. 

Let the Line ^£ # reprefent the horizontal Plane or Way on which a*Pl-i5.F.is>. 
Wheel, reprefented by the Circle !Chg y is to roll from a towards K m y 
n y 0, reprelent three immoveable Rubs* whole Eminences or Tops reach, 
as high as the Points dgh y while the Power draws the Wheel in the Line 
of Direction cG. To know what the Intenfity of the Power muft be in 
proportion to the Intenfity of the Weight (that is, in proportion to the 
Weight of the Wheel) we may fuppofe a bended l eaver in the faid 
Wheel, and are to confider its Effefl: in the Operation $ which being well 
examined will give us this general Rule for all Cafes of a Wheel going 
over a Rub on an horizontal Plane, the Line of Direction drawing along 
the Center of the Wheel being alfo fuppos'd horizontal. 

When the Circumference of a Wheel moving vertically on an horizon- 
tal Plane touches the Top of a Rub, 

the Weight : 

Is to the Power that can draw the Wheel over the Rub 
As the Sine of the Angle y which a Line drawn from the Center of the Wheel 
to the Top of the Rub y makes with the horizontal Line : 
To its Cofwe* 

Z 2 Pre pa- 




Annotate 
Left. III. 



PI 15.F.1P. Through ^ the Top of the Rub 70^, and through g the Top of the 
Rub ng draw the horizontal Lines edt 7 rgs 5 draw the Radii cd, cgm& 
ch 7 the laft of which is parallel to the Horizon and mud be produc'd as 
far as p ; with the Radius cd and Center d draw the Arc ck 7 then from 
the Points d and g draw i/£ and gi perpendicular to ch, and rounds' for 
a Center draw the Circle C*Y)d equal to C/#, which will reprefent . the. 
Wheel rais'd up upon the Top of the Obftacie or Rub m d. 

Demonstration. 

In refpe£t to the Rubify, cde is a bended Leaver whole Fulcrum is d' 
and Brachia cd 7 de % but as the Power draws obliquely to the Brachium 
dc in the Line pc 7 the Brachium dc mud be reduced to fd perpendicular 
to the Line of Direction (being the acting Diftance of the Power) but de 
preferves its whole Length, becaufe cq the Line of Direction of the 
Weight goes thro 5 its Extremity e. Therefore here the Weight and the 
Power will be to one another reciprocally as the Brachia fd and de ^ but 
f d is the Sine of the Angle fed (■= cde) which the Line cd makes with 
the horizontal Line de or its Parallel cf 7 and de its Cofine. Zs. D* 

Scholium, 

If the Rub had been ng, twice as high, the Difficulty of drawing the 
Wheel over it would have been more than twice as great ^ becaufe in 
conlidering the bended Leaver cgr a£ling in that Cafe, it muft have been 
redue'd to another bended Leaver ig r, in which the Power : is to the 
Weight :: as rg : to gi 9 where the Dilproportion of the ailing Diftance 
is more than doubly encreas'd to the Dilad vantage of the Power. 

COROLLARY I. 

Hence follows, that the Difficulty of a Wheel to go over a Rub en- 
crealeth in a greater Proportion than the Height of the Rub ; the Rubs 
of different Heights compared together being always as the vers'd Sines of 
the Complement of the Angle of Inclination, when the Power : is to the 
Weight :: as the Sine Complement : to the Sine of the Angle of In- 
clination, which laft Ratio encreaies fafter than the verfed Sines. 



CORQL- 



A Courfe of Experimental Philofophy. 175 



Annotat 

C 0 R 0 L L A R T II. Led. JIL 

Hence follows alio, that a Wheel cannot by any Power, how great lb- 
ever, be drawn over a Rub whole Top is as high as the Axis (as for ex- 
ample the Rub oh r becaufe in that Cafe the Sine Complement is become 
the whole Sine ch and the right Sine is vanilh'd \ or, what is evident by 
the Scheme, the Power draw£ againft the Fulcrum where it can have no 
Effeft at all; let its Intenfity be ever fo great - 0 unlefs the Direction of the 
Power be made to alter, and it Ihould draw upwards: Therefore in Praftice, 
cfpecially where Carriages are to go upon rough Ways, it is ufual to make 
the Horfes or Oxen draw a little upwards from the Center of the Fore*. 
Wheels. 

COR O LL ART II£ 

Hence likewife may be feen the Realbn why high Wheels go over Rubs 
more advantageoufly than low ones, and that in proportion as they are 
higher becaufe the Lengths of verled Sines being (ceteris paribus ) as the 
Diameters of the Circles to which they belong : That Rub, whofe Height 
was the verled Sine of an .Arc of a certain Number of Degrees in a let 
fer Circle, will be the Sine of an Arc of fewer Degrees in a greater, in 
proportion as it is greater $ therefore the Sine Complement or horizontal 
Brachium of the bended Leaver bearing the Weight, will be lefs, and the 
Sine of Inclination or perpendicular Brachium of the Leaver, to which the 
Power is applied, will be greater. Befides, the high Wheel will not only 
go over Rubs impoffible to the low Wheel, but feveral other Rubs ftill 
higher, provided their Height be not equal to the Semidiameter of the 
great Wheel. As for example in Fig. 20 % the Intenfity of the Power*PU5*F.£§> 
P drawing the great Wheel C D over the Rub D along the horizontal 
Line ah is but half the Intenfity of the Power p drawing the little Wheel 
eg over the lame Rub at g : Becaufe it is not the bended Leaver igr 9 
which is transferr'd from the little Wheel to the great one at FDE, but 
the Leaver fd e, whereby the little Wheel is drawn over a Rub only of 
half the Height. So in Fig. 19. f, the great Wheel, Part of whofe Cir- 
enmference is reprefented by the Semicircle LHf, goes over the Rub MD 
with the fame Eafe, that the little one goes over md\ over the Rub NG 
(impoffible to the little Wheel) with the fame Eafe that the little Wheel 
goes over ng 7 and has no Rub impoffible to it (fuppofing the Intenfity 
of the Power fufficiently great) till it becomes, of the Height OH equal 
to its Semidiameter. 

COROLLAR T IV. 

Laftly^ we may obferve from what has been faid upon this Subjeft, that 
the greateft Difficulty to bring a Wheel over, a Rub is in the firft Effort^ 

and . 



1.74 ^ Courfe of Experimental Philo/bphy, 



Annotat. and that the A&ioh of the Power becomes continually eafier as the Wheel 
Left. III. riles, whether the Wheel was at Reft or in Motion jnlt as it began to 
^^y^j prefs upon the Rub - 0 for the horizontal Brachium of the Leaver as e d 
PL 15, F. 19. (({jppofing md the Rub) rifing continually round the Mdcrum d, when the 
Wheel is rifing from Chgql to *Ddr, diminiihes its a&ing Diftance as 
the Line of Direction cq of the Weight comes from cq to kd, whilft tht 
Brachium df by which the Power a£is continues the fame, as the Line of 
Direftion of the Power goes from the Situation cp into the Situation 
for the Diftance of the Horfes or Oxen, &c. is fo great in proportion 
to^ the Height of the Rub, that we need not look upon the Point * as 
rais'd at all above the Horizon ^ nay, if the Horfes draw a little upwards, 
every Advance of the Line of Direction of the Power towards the Point % 
will be a more advantageous Situation of it. 

From this laft Confederation it appears, that when a Wheel, as Clq, 
goes over a Rub as md or ng, we are not to confider it as if it roll'd up 
an inclin'd Plane as qd or qg, where the Power drawing horizontally (as in 
the Cafe of the Wedge) ails uniformly and that, in the Ratio of the Bafe 
to the Height \ the Power here being require! to exert much more Fore© 
at firft, and lels afterwards. 

12. C50. — — How much the Power mufl he encreas'd in proportion to the 
Angle ^ which its Line of Direction makes with the Plane, will be Jhewn in 
the Notes.'} All this has been fully confider'd in the feveiich Annotation 
to this Lefture. 

13. [62 — — - This fort of Thread is not us^d in W*ood; but in If on and 0- 
ther Metals it is of good Service, being commonly more durable, and raiftng 
the Weight with more eafe than the Sharp Thread, as will be more fully 
Jhewn in the Notes.'] The Square Thread is feldom or never made ufe of 
in Wood, becaufe then the prominent Parts of the Screw, llich as P, N, 

PI. 11. F.11.L, H, Q, O, M, K, I (Plate 11, Fig. 1 i.) would have no more Strength 
than the lateral Cohefion of the Fibres of the Woodi, for a Length very 
little greater than the Thicknefs of the Thread all the Way 5 fo that in 
very great Strains the Arbor abed might be ftript of its Thread ail the 
Way, and lb let go what it was intended to hold. But to prevent this 
Inconveniency the hollow'd Part of the Screw is made fliarp dole to the 
imaginary Arbor or included Cylinder, which thickens the Thread of the 
Screw next the Arbor ^ but then of conlequence it muft come to a jfharp 

PL 11. F.14. Edge on the outfide. This may be feen in the 14th Figure, where, inftead 
of the hollow B A C D, you have bad. 

Tho' by this means the fharp- threaded Screw is ftrongeft in Wood, it 
is weakeft in Metals, where the Thread is generally fine , for if the Male 
and Female Screw do not exaftiy fit, but have a. little too much Play, the 
Sharp Thread of the one will gu'.l (that is, cut and wear away) the" Sharp 
Thread of the other. Whereas in a Square Thread, tho' there ihould be 
fome Play, there is no unufual wearing out, a Flat bearing upon a Flat, 

BefideSj 



A Courfe of ^Experimental Thilofophy. 175 



Befides, on the Sharp Thread the Weight endeavours to defcend (and there- Annotafc 
fore refifts) with more Force than on the Square Thread j becaule, be-Iieft. III. 
fides the Endeavour of the Weight to Aide back on that inclined Plane w^V""^ 
which makes the Afcent of. the Screw (which has been already explained 
in defcribing the inclined Plane and Wedge) it has alfo an Endeavour to 
defcend along another Plane (as ad Fig. i^^) which makes the Sharpnefs*Pl-i 1^.14. 
of the Thread, and confequently the Power muft be encreas'd on that 
Score. 

^ To eftimate what is the Force which the Sharp Thread has to bear 
the Weight on account of its Declivity, let us examine the Screw CDF*P'«^^^ 
EM^fuppofing a Female Screw to be rais'd with all the Weight, which 
confequently muft prefs upon the Thread of the Male Screw here repre- 
sented at CIKPG H, &c. which we will all reduce to the PrefTure on 
the Point P, W A BP being fuppos'd the Weight preffing, and WP its 
Line of Direction. Now, if we refolve the Force W P reprelenting the 
Preflure of the Weight downwards into the two Forces W A and W B t 
of which the firft reprefents the Force exerted againft the Declivity A D., 
and the laft that whereby the Weight endeavours to go along A D with- 
out preffing againft it-, it will appear (becaufe A&ion and Reaction are e- 
qual, *hat the inclin'd Sharp Thread only lifts the Weight with the Force 
reprefented by AW, whilft the Force left, viz. WB, carries down the 
Weight in the Direffion AD, thereby drawing the oppofite Side of the 
Thread of the Female Screw to prefs the harder againft the Thread of 
the Male Screw at C, M and E, &c. So that if the Weight does not 
happen to rife perpendicularly (which it does not in many Cafes) there 
will be a great Encreafe of Friction on the upper Side of the Screw. 

^he-ftriUion of the Screw being owing to many Caufes, we fhall confider it 
in another Place. 

14# £ 70e — Pretenders to Perpetual Motions, and thofe who fromife 
greater Effects by Machinery than is conformable to the reciprocal Proportion 
between the Intenfities of the Powers and Weights and their- Velocities^ 
About the Years 1720 and 172 1, the late Mr. John Rowley, Mathemati- 
cal Xnftrument-maker, talked fo much of the Wheel which he had feen at 
Heffe-Caffel (which he believ'd to be a perpetual Motion, as well as a 
great many Perfons in that Country) that befides the common Herd of 
Perpetual Motion Men, which every Age affords, fome very ingenious Men 
made an Attempt that Way, and were countenanc'd in it by fome great 
Mathematicians, who, when the Scheme was laid before them, declared 
they knew no Re-afon why it lhould not do. But as I always declared 
againft all Projects tending that way ? I was defir'd at that time to pubiifh 
my Reafons why the Thing feem'd impoffible or impra&icable which 1 
did in the Philofophicai Tranfadfions * in fuch a manner as might difftiade* No. i*>9> 
People at firft from any fuch Attempts, in which fb much Time and Mo- 
ney have been lolV I have here printed the. whole Account again ^ but 

defirQ - 




ij6 A Courfe of Experiment a 



Annotat. defire my Reader firft to look over what I have faid In thefe Notes, Page 
Lea. III. 146 and 147, 0 

W^-V-s* The Wheel at Hefle-Caffel made by Monlieur Orfireus, and hy him calTd 
a Perpetual Motion, has of late been fo much talk'd of on account of its 
wonderful Phenomena, that a great many People have heliev" d it to be a£lu« 
<ally a felf-moving Engine; and accordingly have attempted to imitate it as 
fuch. Now y as a great deal of Time and Money is /pent in thofe Endeavours^ 
I was willing (for the fake of thofe that try Experiments with that View) 
to Jhew that the Principle which moft of them go upon is falfe, and can by 
no means produce a perpetual Motion. 

They take it for granted, that if a Weight defending in a Wheel at 
a determinate Diftance from the Center, does in its Afcent approach near- 
er to k fuch a Weight in its Defcent will always preponderate, and caufe 
a eight equal to it to rife, provided that Weight comes nearer the Center 
in its Rife ; and accordingly, as itfelf rifes, will be overbalance by another 
Weight equal to it ; and therefore they endeavour by various Contrivan- 
ces to produce that Effed, as if the Confluence of it would be a per- 
petual Motion. 

But I fliall ihew* that they miftake one particular Cafe of a general 
Theorem* or rather a Corollary of it for the Theorem itfelf. The The- 
orem is as follows : 

If one Weight in its Defcent does (by means of any Contrivance) caufe an- 
other Weight to afcend with a lefs Momentum or Quantity of Motion than 
itfelf) it will preponderate and raife the other Weight. 

Cor, I. Therefore if the Weights be equal, the defcending Weight 
muft have more Velocity than the afcending Weight, becaufe the Momen- 
tum is made up of the V^ight multiplied into the Quantity of Matter, 

COROLLARY II. 

Therefore if a Leaver, or a Balance, has equal Weights faften'd or 
hanging at its Ends, and the Bracbia be ever fo little unequal, that Weight 
will preponderate, which is fartheft from the Center. 

Scholium. 

This fecond Corollary caufes the Miftake ; becauie thole, who think 
the Velocity of the Weight is the Line it defcribes, expeft that Weight 
fhall be overpois'd which defcribes the fhortefi: Line, and therefore con- 
trive Machines to caufe the afcending Weight to defcribe a fhorter Line 
than the defcending Weight. As for example, in the Circle ADB« 
* Pl.i<S/F.r 2 •*) the Weights A and B being fuppos'd equal, they imagine, that if 
by any Contrivance whatever, whilft the Weight A defcribes the Arc A a, 
the Weight B is carried in any Arc, as B £, fo as to come nearer the 
Center in its riling than if it went up the Arc B D } the faid Weight 

fhal 



A Courfe of Experimental Philofophy. 177 

ihall be overpois'd, and confequently by a number of fuch Weights, a per- Annotat. 
petual Motion will be produced. Left III 

This is attempted by feveral Contrivances, which all depend upon this C^fSJ 
falfe Principle ; but I lhall only mention one, which is reprefented by 
Figure 4, where a Wheel having two parallel Circumferences, has the Space 
between them divided into Cells, which being curv'd, will (when the 
Wheel goes round) caufe Weights plac'd loole in the faid Cells, to defend 
on the Side AAA, at the outer Circumference of the Wheel ^ and on 
the Side D to afcend in the Line l&bbb, which comes nearer the Center, 
and touches the inner Circumference of the Wheel. In a Machine of tihis 
kind, the Weights will indeed move in iuch a manner, if the Wheel be 
turnd round, but will never be the Caule of the Wheel's going round. 
Such a Machine is mention'd by the Marquis of Worcefier, in his Century 
of Inventions in the following Words, N°. 55. 

" To/provide and make that all the Weights of the defending Side 
« of a Wheel fliall be perpetually farther from the Center than thofe of 
" the mounting Side, and yet equal in Number, and Heft to the one Side 
" as the other. A m<3ft incredible Thing, if not feen j but try'd before 
" the late King (of bleffed Memory) in the Tower by my Direaions, 
" two Extraordinary Ambaffadors accompanying his Majefty, and the Duke 
" of Richmond, and Duke Hamilton, with moft of the Court attending him. 
« The Wheel was fourteen Foot over, and had forty Weights of fifty 
" Pounds apiece. Sir milium Balfore, then Lieutenant of the Tower 
" can juftify it, with feveral others. They all faw, that no fooner thefe 
" great Weights pafs'd the Diameter Line of the lower Side, but they 
" hung a foot farther from the Center ; nor no fooner pafs'd the Diameter 
" Line of the upper Side, bud they hung a Foot nearer. Be pleas'd to 
" judge the Confequence. 

Now the Confequence of this and fuch like Machines, is nothing like a 
perpetual Motion ; and the Fallacy is this. The Velocity of any Weight 
is not the Line which it defcribes in general, but the Height it rifes up 
to, or falls from, with refpea to its Diftance from the Center of the 
Earth. So that when the Weight (Fig. 2 . *) defcribes. the Arc Aa, its*Pl.id.F.s. 
Velocity is the Line AC, which fhews the perpendicular Defcent (or 
meafures how much it is come nearer to the Center of the Earth) and 
likewife the Line B C denotes the Velocity of the Weight B, or the Height 
that it rifes to, when it alcends in any of the Arcs B b, inftead of the Arc 
BD: So that in this Cafe, whether the Weight B in its Afcent be brought 
nearer the Center or not, it lofes no Velocity, which it ought to do, in 
order to be rais'd up by the Weight A. Nay, the Weight in riling near- 
er the Center ot a Wheel, may not only not lofe of its Velocity, but be 
made to gam Velocity in proportion to the Velocity of its counterpoising 
Weights, that defcend in the Circumference of the oppofite Side of the 
Wheel ; for if we confider two Radii of the Wheel, one of which is ho- 
rizontal, and the other (faften'd to and moving with it) inclin'd under the 
Horizon in an Angle of to Degrees (Fig. ? . f ) and by the Defcent off PI. ,<.p. 3 . 

A a the 



ACovrJe of Experiment '£ Phikfophy. 



Annotat. the End B of the Radius BC, the Radius CD by its Motion caufes the 
Left. III. Weight at O, to rife up the Line p P, which is in a Plane that flops the 
i/YV 1 laid Weight from -fifing in the Curve D A, that Weight will gain - Velo- 
city, ..and in the Beginning of its Rife it will have twice the Velocity of 
the Weight at and confequently, inftead of being rais'd, will oyerpoife, 
if it be equal to the laft mentioned Weight. And this Velocity will be 
fo much the greater, in Proportion as the Angle ACQ is greater, or as 
the Plane P p (along which the Weight D muft rife) is nearer to the 
PL io. F. 2. Center. Indeed if the Weight at B {Fig.. 2.) could by any means be lift- 
ed up to and move in the Arc p> b, the End would be anfwer'd be- 
caufe then the Velocity would be diminilh'd, and become p>C 

Experiment. Fig. 3. 

Take the Leaver BCD, whole Brachia are equal in Length, bent. in 
PI 1$ F ".an Angle of 120* at C and moveable about that Point as its Center : In 
° this Cafe, a Weight of two Pounds hanging at the End B of the hori- 
zontal Part of the Leaver, will keep in Mquilibrioz Weight of four Pounds 
hanging at the End D. But if a Weight of one Pound be laid upon the 
End D of the Leaver, fo that in the Motion of D along the Arc p A 7 
this Weight is made to rife up againfi the Plane Pp (which divides in 
half the Line A C equal to CB) as having twice the Velocity of it, when 
the Leaver begins to move. This will be evident if you let the Weight 
4 hang at D, whilft the Weight 1 lies above it : For if then you move 
the Leaver, the Weight 1 will rife four times as faft as the Weight 4. 

PI iz F * 1 ^ . [go. _ — -—Ifhc Weight and Gibbet would run back and reft over W 3 
°* &c] In the third Figure of Plate 1 2 CGrgs reprefents the Top of the 
Gibbet with its Pulley at r its Extremity, and its Center (or the Top of 
its Axis) at C. It is to be obferv'd here, that the horizontal Part of the 
Rope Cr is in the fame Plane with the middle Line of the Gibbet, or 
that the Rope Cr is parallel to the Lin€ Cr (under it) in the Gibbet. 
Now if it was poffible for the Rope to continue parallel to the faid Line 
Cf in the middle of the Top of the Gibbet, whilft it is movM to the 
left fucceffively in the Situations C<5, C7, C 8, or to the right in the Si- 
tuations Cr, C2, C3, C 4 , C5, the Guider, or Perfon who pulls and 
direfts the Guide-rope faften'd at the End near g ? would bring the Weight 
to any Place on the Wharf on either fide the Crane without any more 
Labour than what overcomes the Friftion of the Axis of the Gibbet. 
But when the Pulleys P and Q_ are plac/d at £ and q 7 the middle line of 
the Gibbet advances towards P and Q_fafter than the Rope does, which 
being oblig'd to fold about the Pulleys makes an Angle with the Line 
abovemention'd, as for example, the angle pSn on the le r t Side and q.^t 
on the right, the angle being 16 much greater as tfre Gibbet is more drawn 
back on the Wharf towards the Crane. The Confluence of this is that 

the 



A Comfe of Experimental Pbilofophy, 179 

the Weight (in this Motion of the Gibbet) muft be rais'd in proportion Annotat. 
as the Rope is lengthened by folding about the Pulley, or in the .propor-Left. 1II> 
tion of Qp 3 to C§ on the left, and C? 4 to C4 on the right. Now if 
the Excefs of the lengthened Rope above the Length of the middle Line 
of the Top of the Gibbet be (for example) one tenth of the whole, 
then a Perfon holding the Gibbet by the Guide-iope, in a Pofition which 
makes that Difference, muft fuftain a tenth 0i of the whole Weight, 
.viz. 224 ib in a Ton, too great a Weight for a Man thus employed ^ to 
moie with the Gibbet. Now as this Force gradually encreafes by drawing 
round the Gibbet, it deceives the Man who pulls the Guide*rope, and as 
by a fudden Jerk he has brought on the Weight, he is often forc'd to led 
it go when it comes beyond his Strength, which fometimes proves of dan- 
gerous Confequence, as well to the Perfons loading or unloading as to the 
Goods cran'd up. 

To prevent thefe Inconveniencies, W orkmen have plac'd the Pulleys in 
a different Situation, viz. in the Situation P, fo that ia turning the 
Gibbet to the right, no Part of the Weight will be felt by the^ Guider 
till the Gibbet comes beyond C4 } and in moving to the left, till it comes 
beyond Cc. But then another Inconveniency arifes from this Conftru&ion, 
which is the Reverfe of the other Thing confider'd - 0 namely, that the 
Weight defcends, and conlequently brings on the Gibbet with a Swing, 
which (if unexpected) may likewife do Mifchief. As in large Weights 
thefe Inconveniencies are moft fenfible, Mr. Padmore of Briftol making a 
Crane for Mr. Men (Poftmafter of Bath) to raife Stoneout of a Quarry, 
contrived an Application of the Axis in Peritrochio^ which takes off this 
Danger and Inconveniency. In the firft Figure, a? is a Wheel with Arms,Fl. 12.F.1. 
whole Axis ku has on it a Pinion at which takes the Teeth of an ho- 
rizontal contrate Wheel faften'd to the Axis of the Gibbet whereby one 
Man ftanding out of Harm's Way clofe to the Wheel has fuch Advan- 
tage of Power by means of the long Arms of the Wheel, as to move the 
Axis of the Gibbet with great Eale, notwithftanding the Inequalities 
above mention'd, and alfo to hold the Gibbet in any Pofition without dif- 
ficulty. 

The fame ingenious Workman has made another confiderable Improve- 
ment in another Crane fix'd by the River-fide, whereby Mr. Men lets down 
his Stone into fuch Veflels as come to fetch it away. 

The Crane itfelf is not of an uncommon fort, but a rat-tail'd Crane 
with a double Axis in Peritrochio and two Handles, whereby four Men may 
raife very great Weights \ and then turning the whole Crane about upon 
its upright Shaft, can fix it in any Pofition and let down the Weights 
fpeedily into the Boats or Barges which come near the Wharf to receive 
them. See the 5th Figure of Plate i6 y where you may obferve it to dif-PI.itf F. 5. 
fer from that reprefented in Plate 12. Fig. 4. becaufe the long Neck ofPl. 12.5V4. 
the Crane is here ofpne Piece, and the Power differently applied. But 
this Conftruilion is not new. Neither is it a* new Invention to let down 
Goods after they have been rais'd by a Crane, by preffing an Arch of a 

A a 2 Circle 



i 8o A Courfe 

Annotat. Circle ftrongly upon a Wheel fix'd to the principal Axis, in order to re- 
Lea. III. tard 'and regulate the Defcent by a Friaion encreas'd or diminifh'd at 
y-^V-x. pleafure, as is done in flopping Windmils. The Catch alfo, that hinders 
a Crane or Capftane from going back, is of common Ufe ; but I don't 
know that any one has applied them both together in the fame Crane, fo 
as to depend upon one another, before Mr. Padmore did it, though many 
have done it fince. Therefore I fliall give a particular Defcription of 
this Contrivance, whofe chief Intent is to prevent the great Mifchiefs 
which often happen by the Carelefnefs of the Men employ 'd to raife and 
PI.itf.F.d. let down heavy Burthens by the Ufe of the Crane. The fixth Figure re- 
prefents an upright Sedion of fo much of the Crane as the Contrivance 
abovemention'd is apply'd to. 

A B is the great Wheel, whofe large Axis A moving on two Iron Cen- 
ter Pins fuch as a y receives the Rope, or lets it run down according as it 
is turn'd, by means of the Handles faften'd at C to the leffer Wheel or 
Pinion C, or as it is fuffer'd to turn the other Way by the Gravity of 
the defending Weight when all Obftacles are removU Upon the Axis 
of the Pinion is the Ratchet Wheel Dd, whole Teeth fucceflively re- 
ceive the Iron Catch / F (moveable on a Pin at F on the Iron Standard 
G, and to be rais'd up occafionally by the upright Iron Hh) to hinder the 
Weight from going back when the Handles are loosM. Upon the fame 
Axis behind the Wheel Dd is a wooden Wheel Ep 7 over which hangs 
the Half-ring of Iron OP o with a Groove or Hollow made in it to fit 
the Circumference of the faid Wheel, fo as to retard, or flop, or any 
way regulate the Motion of the Wheel (and confequently of the Axis and 
Pinion C, and the great Wheel and Axis AB which has the Rope V A) 
according as it is more or lels ftrongly prefs'd down to make a Friaion 
on the Wood, as it moves after the Catch is rais'd out of the Teeth of 
the Ratchet. The horizontal Leaver K L governs all thele Motions in 
the following fanner, viz. When the String Q^^ K^ faften'd to the faid 
Leaver at K, is pull'd, the Leaver moving on its Center M, does, by an 
horizontal Pin fix'd at right Angles to its Side at I, raife the Piece tih i 
and confequently releafe the Ratchet by railing the Catch at / out of the 
Teeth : Then the Weight deicends fwiftly, moving the Wheel and Pinion 
round by its Force $ but to prevent the too fwift Defcent, the Leaver is 
pulfd up a little more ftrongly by the Guider who holds the String Q^K, 
. which brings down the contrary End of the Leaver L, and confequently 
the Iron N, fo low as to make the femicirular Ring O to prels hard upon 
the Wheel Ep, which it did not do when the Catch was rais'd but juft 
out of the Ratchet. N. B. A Jirong Pull flops the whole Motion, and a 
more gentle one regulates the Defcent. And if the Guider fhould be care- 
iefs and let go the String \ then immediately the Spring Ss 9 whof^ End 
s had been deprefs'd by the End L of the Leaver, will raife it up again 
(by its lateral Pin X) and reftoring the whole Leaver to its firft horizon- 
tal Pofition, the other lateral Pin I in the long Arm MK of the Leaver, 
will through the Notch H, prefs upon I the lower End of the upright 

Piece 



A Courfe of Experimental Phihfophy. iSr 



Piece Uh, and fo bring down the Catch Ff into the Ratchet Wheel at Annotat. 
/, the curved Piece O P/> at the fame time flying up and no longer pref Left. III. 
iing the wooden Wheel Ep. KS~V"\J 

Thus will Mifchief never be the Confequence of Carelefiiels, becaufe 
of the Catch ; nor will the Weight go down by jerks, which would have 
been the Confequence of the Catch us'd without the Half-Ring, becaulePLitf.F.& 
the Catch is lifted quite out of the way when the Half-Ring is brought 
down and applied by pulling the String at N. B. T, * j, tz is part 
of the upright Seftion of the timber of the Frame. 

To make this the plainer, let us examine the 7th Figure of Plate 16 ;Pl.i& F.7. 
where we have an horizontal Se&ion of the Parts above mention'd. 
T*T is Part of the Timber of the Frame. BB is the great Wheel, 
whole Axel that holds the Rope is mark'd AAA, and its Iron Axis 
goes thro Bell- metal Boxes at a a. CC is the Small Wheel or Pinion, 
whale Axis is .£ f.- PD is the Seftiqn pf the Ratchet Wheel made of 
Iron. Between the prick'd Lines Ap and Ei is luppos'd the wooden 
Wheel upon the Axis of the Pinion (not drawn here to avoid Confufion, 
no more than the femicircular jprefling Piece mark'd OP<? in the laft Fi- 
gure) the Bafis of whole upright fix'd Supporter is reprefented by R, 
and the End of the Piece which brings it down upon O,ccafion is ftjewa 
at N. KL is the horizontal Leaver, whofe Center is at M, moving 
vertically by a Pull of the String ftften'd t<? k at IL H is the firft late- 
ral Pin of the jLea^er, which .at I goes thrw^h the bottom of the JPiece 
JH, Raifer of the Catch F/, already defeib'd with its Supporter (3, on 
whole Top the Catch moves by a Center Pip. ApAte the leeond "late- 
ral Pin of the Leaver, whofe Office is to prefs upon the End s of the 
crooked Spring $s faften'd to the bottom of the Frame at the farther End 
S. So that when the End K of the Leaver is pull'd up, the End L 
which is deprds'd, mii be lifted up again into its Place by the Force of 
the Spring reftoring it feif. 

N. B. "The crooked Figure of the Spring, and the Manner bf its lifting the PL itf. 
Pin is beft Jhewn in the laft Figure. 

There is a fine Contrivance of an inclined Waggon- Way made of Tim- 
ber to bring down the Stone homMw Men's Quarry to the River's Side^ 
the Diftance of near a Mile, in Waggons which come down the Decli- 
vity on the artificial Way by their own Gravity, as the Coal-carriages do 
near Newcaftle. But this Waggon-way differs quite from thole in the 
North, every Part being very much alter'd for the better, and the Car- 
riages themfelves contrived to carry much more Weight without Danger. 
the Defcription of this Contrivance, wherein Mr, Allen and his Workmen 
have Jhewn great Skill and Ingenuity, I wtift mow o#it md give, it in aw 
tker Part of this Book. ~ ' 



L E C- 



i8s 




LECTURE IV. 



Concerning the Frifiion in Mechanical Engines. 

1 e£t IV \ "% T ^ ^ ^ * * iave ** a ^ hitherto in the Three firfl: Lectures 
^✓Vx/ V/V and their Notes, is diffident for explaining the Princi- 
1 T If pies of Mechanicks (ftri&ly fo call'd) enough to fet 

People to work, who have a Genius for Practical Arts ; but as 
they may be guilty of confiderahle Errors without making proper 
Allowances for Fri&ion, and knowing how to find out (nearly) 
what it is in Engines already made, and fuch as they intend to 
make -, I thought proper in this Place to give a Le&ure on 
what I have been able to difcover of the Nature of Fri&ion, by 
reading all the Accounts I could meet with on that Subject, by re- 
peating feveral Experiments already made the better to confider 
their Circumftances and whether the Accounts of them were true ; 
and likewife by making a great many new Experiments my felf. 

Tho } there are fo many Circumftances in the FriBion of Be- 
dies, that the fame Experiment' does not always fucceed with 
the fame Bodies „ fo that a Mathematical Theory cannot beeafily 
fettled ; yet we may deduce a Theory fuffcient to direcl us in 
our TraBice from a great Number of Experiments j always ta- 
king a Medium between Extremes. . 

First then, it is obferv'd that Wood, Iron, Brafs, Copper 
and Lead, when greas'd or oiPd (as is done in Engines) have near- 
ly the fame FriQrion, and therefore the fame Rule will ferve for 
all thofe Subftances. For tho' one may at firft imagine that Me- 
tals muft needs flip over one another more eafily, becaufe they 
may be made fmoother and will take a better Polilh ; yet it is 
found by Experience that the flat Surfaces of Metals or other Bo- 
dies may be fo far poliflfd as to encreafe Friclion ; and this is a 

mecha- 



A Courje of ' Experiment "alThih/ophy. i8g 

mechanical Paradox ; but the Reafon will appear when we con-Left. IV. 
fider that the Attraction of Cohefion becomes fenfible as we bring u/VsJ 
the Surfaces of Bodies nearer and nearer to Conta£L This is ve- 
ry evident in drawing Glafs Plates over one another, which re- 
quires more Force than if they were of Wood, and the fame is 
true in Metals , for tho' the Preffure of the Air is fometimes a 
little concerned in this Phenomenon, yet the Attraction of Cohefion 
does fo far exceed it, that we need not take notice of the Effed 
of that Preffure in the A£tion of the Parts of an Engine on one 
another. It is true indeed that a couple of Marble Plates fUck to 
each other by the Preffure of the external Air, when being firft" 
oil'd, to exclude the Air from between them they have been flipped 
upon one another ; and that when fufpended in the Receiver of an 
Air-Pump they fall afunder as foon as the Air is drawn out of the 
Receiver. But if they be made very fmooth, they will cohere 
flrongly even after the Preffure of the Air is wholly taken off by 
the Air-Pump. I have applied together the flat Surfaces of two 
fmall Cryftal Buttons, without wetting or oiling, which have 
coherM fo ftrongly as to hold 19 Ounces Troy before they were 
feparated, when their Contact w T as but a Circle of one r th of an 
Inch in Diameter; in which Cafe the Preffure of Air could not be 
greater than the Weight of an Ounce ; becaufe a Column of Air, 
whofe circular Bafe is one 1 sth of an Inch in Diameter weighs no 
more. In Metals the fame is evident ; but more efpecially in Lead ; 
for two Balls of Lead of about one or two Pound Weight each, 
if parM clean with a Knife and applied clofe together, fo as to 
touch in a Surface of about one icth of an Inch in Diameter, will 
flick together fo as not to be feparated by a iefs Weight than of 
40 or 50 Pounds, tho' the Preffure of the Air in that Cafe could 
not amount to one 4 th of a Pound. See ThiL Tr an/a St. N. 389. 
But to return to our Experiments of Fri£tion. 

Experiment I. PL 13. Fig. 1 8. pI - ^F- iB - 

Ch is a fmooth Piece of Wood one Inch thick, four Inches 
wide and fix long, with a little Hook in its Forepart and weigh- 
ing fix Ounces. If it be drawn along an . horizontal Plane repre- -.. 
fen ted by the Line AB over the Pulley P by means of the String 
H W, the Weight W equal to two Ounces and as much more as 
will overcome the Friction of the Pulley ? will draw it along whe- 



1 84 A Courfe of Experimental PMlofophy. 

Led. IV. ther it Aides on its greateft Surface or Flat as at c, or on its Edge 
iS~\Ts) as at K, tho* in the laft Cafe there is only a fourth part of touch- 
ing Surface. From hence it appears that the f rift ion is equal to 

* Am, 1. a fj 0 ut one ^d of the Weight 'y* and an fes from the Weight that prefi 
fes the Tarts together, and not from the Number of Tarts that 
touch ; for whether the Parts of the Surface be confider'd as Springs 
to be bent, or as fmall Eminences over which the Body drawn muft 
be lifted, it is plain that the Difficulty will be the lame, whether 
the Surface be greater or lefs, provided it be prefs'd: in a recipro- 
cal Proportion of its Bignefs ; for tho' the Bafe of c be four times 
broader than the Bafe of K, every Inch of it in Breadth is prefs'd 
but by one Inch of Wood in Thicknels; whereas the Surface on 
which it refts in the Pofition K, which is four times narrower, is 
prefs'd by a Thicknefs of -Wood of four Inches. The Friction 
therefore, or Impediment to the drawing the Body in the Line A B, 
arifes not from the Number of Parts which touch, but from the 
PrelTure on the touching Surface, as appears yet more plainly from 
the following 

pi.i 3 .f.i8. Experiment II. PI. 13. Fig. 18. 

Let the Pulley vr (over which the "Vy eight w W) drew 
along K, when it was rais'd up to the Level of m the Hook of 
K above A B) be brought down to the fame Level as P, then 
w = W will not draw K along without the Help of the little 
additional Weight q ; becaufe the Tra&ion made in the oblique 
Direftion mp makes K prefi more againft the horizontal Plane 
than when the Draught is in the Direction m it ; but if the Hook 
be fix'd at n fo as to make the Line of Direction parallel to the 
Plane AB, then will the Weight w, without the Help of q y draw 
K along as W did c. 

n 13.R ij. Experiment III. PL 1 5. Fig. 19. 

Upon the Table or horizontal Plane T M N O, let a circular 
Plane or Plate of about two Foot Diameter move, bearing on a 
Pin round the Center C fo as not to touch the firft Plane ; then 
let a Brafs or Leaden Plate, fuch as A, B or D, be fo laid betwixt 
the circular Plane and the Table, as to prefs upon th&,Table with 

all 



A Courfe of Experimental Philqfophy. i 85 

all its Weight, and at the fame time (by means of a Pin rifingLeffc. IV. 
from its middle) be carried round along with the circular Plate yv\* 
under the Point A, B or D. Then if the Weight of the Plate A 
be equal to 30 Ife, a Force equal to to lb will draw the Plate 
round pulling in the Dire&ion AT, when the faid Plate is placM 
at A or D ; but if the Power draws in the Line B t or E r Tan- 
gent to the little Circle B E, it will require 20 ife to draw A round : 
Laftly, if the Power draws from A towards T in the Tangent 
of the great Circle A£tD, whilfl; the Plate is fix'd^at B, then a 
Force equal only to 5 ife will move round the Plate, 

This fhews that the Fri£tion is encreasM when the rubbing 
Parts move fafter, and decreased when they move flower than the 
Power. Therefore we may fay that the Refinances from FriBion 
are to one another in a Ratio compounded of the Treffures of the 
rubbing Tarts, and the Times or Velocities of their Mo- 
tion 

When a fmooth Body is laid on an inclined Plane, according 
to the Laws of Mechanicks it ought not to reft upon it, but mult 
Aide down. But the Fri&ion being equal to one 3d of the Weight, 
as we have already fhewn, the Body" K* laid. on the inclinM Plane* M-*3-F-*>. 
AB will not Aide down till the Perpendicular AC be the third 
part of the Bafe B C ; becaufe then the Body's Tendency down- 
wards in a Line parallel to A B is equal to one 3d of the Weight 
of the Body. 

Hence it appears how neceifary it is to confider the Fri&ion 
in mechanical Performances ; as for example, if a Beam A B f ly-t Pl.i7.F.x\ 
ing on the rifing Ground D c is to be drawn by a Power at P in 
the Direction AP parallel to D^; when A a the Rife of the Plane 
above the horizontal Line Hb is one 30th of a c, a Power equal to 
one 3 cth of the Weight would be able to draw it along accord- 
ing to the Laws of Mechanicks exclufive of Fri&ioh ; and there- 
fore ico ife would draw along a Beam of 3000 ife along the Plane 
A c : But as the Fri&ion is equal to one 3d of the Weight, we 
muft have a Power equal to f 00 ib -f- 1000 ife before we can 
draw the Beam along, if the Plane was as fmooth as a Marble 
Floor. But along the Ground, w r here even the fmootheft Earth is 
rough, a much greater force will be required. Monf Amontons 
of the Royal Academy at Taris found that a Force equal to 
2250 ife was but fufficient to draw fuch a Beam up a Hill of the 
Afcent abovemention'd. 



Expe 



1 86 A Courfe of Experimental PMItrfophy. 



Le£L IV. 

pi n Experiment IV. PL 1 4. Fig. 2 y 3 and 4. 

Let A B a wooden Cylinder of an Inch Diameter, fmooth and 
well polifh'd, turn freely on two Supporters S j, likewife .fmooth, 
well polifhM and greas'd. Then at each End of a filken Thread 
or String thrown over the faid Cylinder, or wound about it two 
or three times (for that makes no difference if the Parts of the String 
do not touch one another) fufpenda Weight of 9 ife, which Weights 
will keep each other in JEquilihrio* Then adding feveral Weights 
to the 9 ife Weight? here made ufe of as a Power, to find exa&ly 
what Addition it muft have to raife the Weight W, which is alio 
only a 9 Ife Weight, that Weight will not be rais'd up by the 
turning of the Cylinder till P and all the Weights added to it 
make all together 18 ib. This is agreeable to what was fliewn 
before by the firffc Experiment of this Lefture. F©r as the whole 
Weight that prelTes the Cylinder on its Supporters is W -f- P. or 
18 ife, 6 ife muft be added to P in order to overcome that Fri&ion ; 
but that additional Weight adds alfo a Fri&ion of 2 Ife the third 
part of its Preffure, for the overcoming of which Fri&ion 2 ife muft 
be added, whofe Fri£tion requires alfo two gds of a Pound, and fo on, 
in a Series of Fractions as 4 + -h -A, Sfo Now as the Weight 
of the Cylinder itfelf was not confider'd, the proper Way to allow 
for its Fri£Hon, if it be not very heavy, is to double the Power 

♦ P1.I7.F..4 at once, * as appears in Fig. 4,, where A reprefents the Se£tion of 

the Cylinder above mention'd. 

I f the Cylinder has Gudgeons or a fmall Axis, fuch as that re- 

tPl. x7*F-3-prefented. in Fig. c. *\ it will move as much more eafily on its Sup- 
porters as the Diameter of the Axis at G and g is lefs than the 
Diameter of the Cylinder ah\ as here the Weight added to p 
need be but 1 \ ife when the Diameter of the Axis is but £ of 
an Inch j becaufe then the rubbing Parts move flower than the 
Power,, in that Proportion,agreeable to what was fihewn by the third 

IS Pi. 17. F. 4. Experiment of this Lefture. The fourth Figure \ reprefents the 
Se&ion of the Cylinder at a r and of its Axis at g. 

He NCEwe may know what difference there is between the Ufe 
of Sledges and Carts for drawing, along heavy Goods. If the Ground 
was perfectly even like a marble Floor it would require \ of the 

* Ann. 2. Weight of the Sledge, and all that is laid upon it, to dra w it along * 

but as fuch a fkne is not u§M in Pra&ice (and if it could be had, 

Horfes 



A Cottrfe of Experimental Tbihfopby. I 87 



Horfes could not pull well on a flippery Pavement) we muft al-LeQ:* IV< 
ways make ufe of a Power greater than one 3d of the Weight. o^V^o 
But in a Cart,, if the Wheel be fix: Foot high, and the Hole in 
the Knave for the End of the Axel four Inches, the Friftion will 
be diminiftfd 18 times ; therefore a Power equal to 5 - 4 Part of the 
Weight will be able to draw it along upon an horizontal Plane ; 
becaufe the 18th Part of \ is =r 5 \. Sledges therefore fhould on- 
ly be usM where Streets are too narrow for Carts, and where 
Goods in fmall Parcels are to be laid on and taken off often, for 
the Conveniency of the Men ; but the Horfes muft work the 
harder. This alfo fhews that high Wheels in Carriages are pre- 
ferable to low ones on account of their having lefs Fri&ion, be- 
fides the mechanical Advantage which we have confiderM in another 
Place; tho'it is not always expedient to make ufe of them, as for 
example, in Beer-Carts high Wheels would be inconvenient, becaufe 
of the Neceflity of often loading and unloading. 

To reduce all this to Pra£Hce, take the following Rules for cal- 
culating the whole Fri£tion of , Engines. 

R V L E L 

I n examining all the Fri£Uons, begin with that which is near- 
eft to the moving Power. 

R V L E IL 

To find the firft Fri£fcion, confider the Spaces gone through 111 
the fame time by the Power and by the rub Ding Part, and accord- 
ingly take a proportional Part of ~ of the Power. As for exam- 
ple, in equal Velocities of the Power and rubbing Part, the Fric- 
tion is y of the Preffure which is made not only by the Power, 
but by the Refiftance equal to it, and therefore the third part of 
the whole Preffure muft be equal to two gds of the Power. 

R V L E III. 

The Power being unknown, muft firft be found by knowing 
the Velocity of the Weight, % and thence deducing that of the Power* 
by mechanical Principles : Then, by what has been fhewn here* 
finding the Friction, there muft be fo much added to the Power 
to make the Engine work ? always obferving that what has been 

B b 2 added 




Lect. IV. added for the Fri&ion firft found does ftill further encreafe the 
^-^*V~n-' Fri&ion, and therefore there muft ftill be allow'd fomething for the 

Encreafe of Fri&ion caus'd by every new Addition to the Power 
N. B. We muft remember, as has been faid before, that if 

the Power be an heavy Body, its Velocity is its perpendicular 

Afcent or Defcent ; but if of another kind, the Velocity is its Space 

gone through, 

R V L E IV. 

T h e Friction of the feveral Parts of an Engine however re- 
mov'd from that Part to which the Power is applied may be 
found by comparing their Velocities with that of the Power, and 
thence deducing the Fri&ion as has been Ihewn ; and when all 
the particular Fri&ions have been found and added together, their 
Value added to the moving Force will not enable it to overcome 
the Refiftance in a compound Engine any more than a fimple one ; 
for that Addition fuperadds a Fri&ion to every rubbing Part, there- 
fore we muft ftill encreafe the Power as fhewn in the laft Rule. 
An Example will illuftrate both Cafes. 

*Pl.i7.F. 5. The Diameter AB of an Axis in Teritrochio * is equal to 2. 

Foot, and that of its Axel ab only to fix Inches ; therefore if the 
Power P be =: 108 ft, the Weight or Refiftance W will be 
= 648 ife. Here the Friction will be 12 flb or \ of 72 ife if the 

t PI. 17- Fa. Axel befupported on its Surface, as in Fig. Now as 12 is k 
of the Power 1 o Q , there muft be added f of 1 2 to overcome the 
Encreafe of the Friction caufed by -thjs 12 ife, viz. 1 \ % and 
then \ of this laft and fo on ; fo that to overcome the Refiftance 
= 648 ib the Power muft be = 1 08 -+- 12+ r f -+- * 7 , lb or 
more than 121 £ 1K But if the Axel had Gudgeons of Iron CC 
of only one Inch Diameter, the Fri&.ion on them would be fix times 
lefs, the Velocity of their Surface being diminifh'd in that Propor- 

BP1. 17. F. s. tion. Now if there be join'd to the Axel a b another Wheel D E || 
likewife of three Foot Diameter with an Axel of fix Inches F G, 
about which the Rope or Chain that fupports the Weight winds 
infteadof winding about ab r then by mechanical Rules the Weight 
X = 3888 lb will be fuftain'd by the Power P of 108 tb. 

N.B. We here fuppofe the laft Axel FG to have a Ife Iron 
Gudgeons as c of an Inch 'Diameter ^ and that (by means 
af a Strap of a Leather \, or a Ropc^ or Chain going round 

the 



A Courfe of Experimental Pbikfophy. 189 

the Axel ab and the Wheel DE) the fecond Axis in Peri-LecT:. IV 
trochio DFcGE is carried round in the Direction aD, fo as </YV 
to draw up the Weight X, fix times more flowly than it would 
rife if at W. But the beft way is to make ufie of a Tinitm 
with Leaves ft hat is a fmall Wheel with Teeth) to carry round 
the great Wheel by its "Teeth j as here the Tinion of i a Leaves 
on the Axis ab will carry round the Wheel DF which has 72 
Teeth {its "Diameter being fix times greater than that of ab:) 
Becaufe a Ropej Straps or Chain cannot perform its Office with- 
out being made fo tight as not to flip, in which Cafe the Tref- 
fion cans' d by the Elafticity would occafion an additional Friftion? 
befides the additional Refiftance made by the 'Difficulty there is 
to bend the Rope, &c. 

To find the Frittion of this compound Engine, we muff' confi- 
der all the Parts that rub, viz. firft C the Gudgeon with 3 V of the 
Velocity of the Power j then the Teeth or Strap at ab, wih £ of 
of the Velocity of the Power ; and laftly, the Gudgeon c of the 
Wheel DE, with ,f 6 of the Velocity of the Power; which gives 
for thefeveral Friaions IS = 2 ft, V = 1* * and = 
c,333 ZSc. lb : The Sum of all the Frictions therefore is 14,33 3 fifc. ft • 
by which Number if you divide the Intenfity of the Power or t 0 8* 
you will have for your Quotient 7,5 ^ which will give you I 
Divifor for every Weight to be added to the Power on account of 
the Friction When therefore you have added 14,333 &c. for the 
Sum of the Fric1:ions,you muft fuperadd-*^- 3 -^ 1,91 for the Fric- 
tion of the firft additional Weight, and ^J- = 0,2 5 for the Friftion 
of the fecond additional Weight, &c. Therefore in order to raife 
X or 3888 ft by means of the compound Engine here mentionU 
the Power muft not be 108 ft but (24,16 ft -h 

N.B. All other Cafes may be deduced from this. 

Tho\I have, at a Mean „ taken the Friction to be equal to a 
third part of the Weight ; yet by making many Experiments fince, 
I found it much to vary, being (ometimes greater and fomet imes 
lefs i fo that it is fcarce poffible to come at an exact Theory 
Tet for Trail ice, as I have already fiaid, it is ufeful to know 
what Experiments have been made with any particular View 
to direct us in the like Cafes by taking the Mean of the diffe- 
rent Effects we find. As Carriages are Machines of the greaU 
eft conference for the Vfes of Life J I thought it would not be 
unwelcome here* to enlarge upon the Friction of finch Instrument 

b% ~ 



190 A Courfe of ExperitHefttalPM 

Le£L XV. by giving & n Account of fever al Experiments made upon Sledges 
^yyV and Wheel Carriages by Mr. Camus a Gentleman of Lorraine^ 
which I have fnce tried and found to fucceed in the fame man* 
tier in almoft every Trial. The little differences I obferv y d he* 
tng unavoidable in Things of this Nature^ even when made by 
the fame Hand : Therefore I choofe to give the Account of them 
in the Author's own Words - tr inflated from the French^ in 
which Language he publijh*d his Book entitled, Traite des Forces 
mouvantesj pour la Pratique des Arts &: Metiers, &c. Par M. de 
Camus. 

As there will be a Difference in the Fri£Hon of the fame Body 
drawn over different Bodies, it is neceffary as much as poflible to 
know what that Difference is, in order to know how to manage 
or apply Forces. For this reafon the following Experiments have 
been made, in order to find out nearly what Forces or Powers are 
required to draw Weights, or what Force is loft by Fridion, and 
what Metal is moft proper to be us ? d, or what Materials ; that we 
may lofe the ieaft we can of the Force of the Power ; and what 
Effe£t Water, Greafe or Oil have upon different Subftances. 

For this Purpofe, we muft take three Sledges, each of them 
an Inch and an half wide and three Inches long, each Side or bear- 
ing Part being two Lines wide. Different Weights muft be laid 
upon each Sledge, and they muft be drawn over flat Bodies of 
different Subftances or Metals ; and the following Effe&s will be 
produced* 

Take three Plates 2 Inches wide and 4 or 5 Inches long, one 
of Iron, one of Brafs and one of Copper ; let them be draw-fil'd, 
that is, fil'd longwife, without being poliflfd, and rubb'd uponfuch 
a Stone as the Streets are pav'd with, that they may be like the 
Sledges drawn along the Streets, and alfo their Grain may lie the 
fame way as it does in the Holes for Pivots and Gudgeons in Ma- 
chines in regard to the Direction of the Motion. Let thele Plates 
be faften'd upon a little Plank of Oak with a Nail whofe Head 
is off, that they may be put on and taken off eafily one after ano- 
ther by means of an Hole in the End of the Plate. At the End 
of the Board fix a little Pulley with very fine Pivots, and let the 
Copper and Brafs Plate be rubb'd fmooth on one Side with Pu- 
mice-ftone. 



T H E N 




Th e » take a light filken Purfe with a ftrong Silk to run overLe£h tV* 
the Pulley and draw an Ounce Weight (including the Sledge) then v/YNJ 
prepare twenty leaden Balls weighing altogether m Ounce* that 
you may put into the Purfe fuch a Number of them that the Sledge 
and its Load may be drawn upon the different Bodies and Me- 
tals. Let there be alfo prepared *o Balls weighing altogether one 
Pound, to draw fuch a Sledge as fhall together with its Load 
weigh one Pound ; as alfo a third, weighing three Pounds with 
20 Balls equal in Weight to three Pounds, Let the Sledges be 
one of Iron, or armM with Iron, as moft of the Sledges are which 
are drawn along a Pavement of Pebbles ; one of Wood unarmed j. 
the third of Lead, or armM with Lead \ and a fourth, if you will, 
of Brafs or Copper. 

If you put the Balls gently into the filken Purfe (or the great 
ones in a Bag of Linnen) Hopping it fo that it may not move* 
and then the Board be lifted up at the Pulley End, fo as to rife 
an Inch in the Length of two Foot, that the Sledge being once in 
Motion may not run fwiftly, but on the contrary may continue at 
reft when it has been ftoppM in the running foftly at firft ; but it 
muft not be kept long in one Place, becaufe there it would ftick 
or fink in, and more Force would be required to fet it going at 
one time than at another. If the Board was fet horizontal, or 
inclining towards the Pulley, the Experiments would not fucceed ; 
becaufe the Sledge being once fet a going would run all at once : 
And therefore we found the beft Situation of the Board was to 
have it rife a little towards the Pulley, and to fet the Sledge a 
going. Things being thus prepaid, the Effe£fc of the Experiments 
was as is exprefsM in the following Tables. 

The firft: Column fhews the Number of Balls required to draw 
the Sledge dry upon different Subftances or Metals as fet down. 
Thus Iron upon fFood, fignifies the Sledge arm'd with Iron, Ai- 
ding upon the wooden Board : Iron upon Iron, the fame Sledge Ai- 
ding upon the Iron Plate ; and fo of the reft : Vj>on polijh'd Brafs^ 
fignifies the fame Sledge Aiding upon the Brafs rubb'd with the Pu- 
mice-ftone : And upon polijtf d Copper the Copper Plate rubb'd 
with the Pumice-ftone. 

Th e Columns over which are the Words — wet — greas'd — 
oiPd — fignify that the Plates and Sledges being wet, greas*d^ or 
oil d, the Sledges were drawn along by the Number of Balls fpe- 
cified according to the Columns. Thus the firft Column, where 

you 




Left. IV. you find thefe Words Iron upon Wood $, above which Number is 
l/YV written Balls, fignifies that the Sledge which weighs three Pounds, 
Aides upon a Board of Oak with 5 ofthofe Balls, 20 of which weigh 
3 Pounds ; fo that there is only required one quarter of its "Weight 
to make it Aide along a plan'd oaken Board : But if that Board be 
wet, 8 Balls will be required/ which fliews the Friction to be en- 
creas'd the Value of 3 Balls : If the Wood be greas'd, .4 Balls 
and a half will do, which is but little more than half of what is 
requir'd when the Wood is wet : If the Wood be oil'd, there mull: 
be 5 Balls; and fo on for all the Columns upon different Me- 
tals. 

We have not fet down the Number of Balls required for draw- 
ing the Weight of one Pound, becaufe the Proportion was found 
the fame as in the 3 Pound Sledges ; at leaft the Difference was 
fcarce perceivable. But for the Sledges weighing one Ounce, we 
give an Account of their Effects, becaufe as they differ from thofe 
of 3 Pounds, we may the better from their Comparifon deduce the 
Caufes of Friction and Refiftance. 



A Table 



A Tab l e of F R I C T I O N S. *^ 



dl Load of three 
and an half 
iongy "with 





ts drawn upon a Sledge one 
in the Under-Plates, and three Inc 



Iron upon Wood 

Iron upon Iron 

Iron upon Brafs 
up n polilhM Brafs 
upon poliflfd Copper 



5 

3 

31 
3 

nl 
0 2 



Wood upon Wood 7 
Wood upon Iron 5 
upon Brafs 4 
upon polifh'd Brafs 4! 
upon polifh'd Copper 5 

Lead upon Wood 
Lead upon Iron 
Lead upon Brafs 



5 

7 

5 

6 

6; 




greas f d- 

greased 

greas'd 

greas'd 

greas'd- 
■j ■ ■ 

greased 
greasM 
greas'd- 
greas'd- 
greas'd- 



Balls 

- 4i 

- 4 

^ 4l 

si 

4 

4l" 

4 g 
4i 



greas'd 
greas'd- 
greas'd 
greas'd- 
greas'd- 



4 
5 
5 

4* 
5 



upon polifh'd Brafs 
upon polifh'd Copper 

A Sledge weighing an Ounce with its Load is drawn along 

with 



Iron upon Wood 

Iron upon Iron 
upon Brafs 
upon polifh'd Brafs 
upon polifh'd Coppei 



Balls 

6 

4 
5 

e\ 

6 





Balls 




Balls 


wet- 


- 5 


oil'd- 


- 8 


wet - 


- 9 


oil'd- 


- 7 


wet- 


- 6 


oil'd- 


- 7 


wet- 


~ 7 


oil'd- 


- 8 


wet- 


~ l\ 


oil'd- 


- 9 



greased 
greas'd 

greasM- 
greas'd 

greas'd- 



Balls 
• 10 
•13 

■ 13 

9 13 



* N. B. ^ lw is one nth Fart of an 



Woo* 





7 

7 
6 



A Cmrfe of 

Balls 

Wood tipon Wood 7 
W ood upon Iron 6 
upon Brafs 5 \ 

1 ' n i' d Bfafs 6 
'd Copper 7 

Lead upon Wood 
Lead upon Iron 
upon Brafs 

upon p^iflfd Br &fs f 
upon pdlih'd Copper 8 

^he forhe liggcr Sledges <with the freight Oj 

istierk drawn upm a Pehbfe, pch m the Mrdets 

withj by Ba u s 

Wood upon Pebble or Paving-ftone 8 \ ^ 

Eton upon Pebble ~— - — — 1 o 1 

upon Pebbles — — - — 1 6 1 1 









Balls 


#et— 


f6 


; oil'd— 


6 \ 


wpf 




oil'd — 


8 


WCl — 


T T 
1 1 


aiPd — 


8 


wet-^ 


J 2 


rvvl- ? i^ — 


PI. 

° 2 


'wet— 


13 


oil'd - 


9 


wet — 


10 


oil'd— 


9 


wet — 


8 


oil'd- 


9 ' 


wet — 


6 


oil'd- 


8 


%ret 
{ Wet— 


& 
8 


. oil'd— 

oil'd— 


9 
10 







wet- 




13 

9 
1 J 




/iff/* Sledges of 

Ball 

Wood lipon Pebble 

Iron upon Pebble 
Lead upon Pebble 

Load if Three Pounds upon a Sledge nohofe Sides are 
brought to a cutting Edge where they bear, inftcad of the 
common Way> 




„v wtth 



:ron upon 
upon Iron 



Balls 
4 



upon £>oliflh*d Brafs 3 
upon pbllftfd Copper 3 f 



Wood upon Wood 1 o 
upon Iron 3 
upon Brafs 3 
upon poliflVd Brafs 4 
&pon polifh'd Copper 5 





Balls 




Balts 


greas'd— 




wet — 


■ 7 


oil'd- 


■ 4 


3 


wet — 




oil'd- 


- 3 


greasM— 


3 


wet**** 




oil'd- 


• _.3i 


greas'd — 


3| 


wet- 




oii'd- 


3 2 


greas'd— 


3'»- 


wet— 


- 31 


oii'd— 


3 2 


greas'd— 


3 


wet- 


• 16 


oil'd— 


: 5 


greas'd— 


3 


wet 


= 7 

- 6 


oil'd- 


- 3 


greased— 


3 


wet- 


oiPd - 


- 3 


greasM — 




wet— 


- 5 


oil'd- 


5 2 


greas'd — 


' 3 s 


wet— 


- 5 


oil'd- 


~ 4i 


greasM— ■ 


3 * 








Am 




An Ounce 




Wfton a Sledge Brought alfo to an Edge, 
<was drawn by 



1 95 



It « O. , X\r 

jucul* ,1>,Y> 



Iron upon Wood 
upon Iron 
upon Brafs 
polifh'd 




er 



Balls 

5 
4 
4 

5 

6 



9 
4 
5 

7 



B;ajls 
wet— 8 
wet — Ah 

wet — 7 < 
wet— 7 
wet — 8 


Balls 

oil'd- 6 
oil'd — 5 
oil'd— 6 
oil'd— 6 
oil'd— 6 


greas'd— 7 
greas'd — 7 
greas'd — 8 
greas'd— 8 
greas'd— 8 


wet — 1 6 
wet— io 
wet — ■ 8 
wet— 8 
wet — 9 


oil'd- 5 
oil'd— 5 
oil'd— 6 
oil'd — 7 
oil'd— 8 


greased— 9 
greas'd— 9 
greas'd— 9 
greas'd— 9 
greas'd — 9 



Wood upon Wood 
upon Iron 
upon Brafs 
upon polifh'd Brafs 
upon poliflfd Copper 

0Gth the fame cutting Sledges 0 haded w&b three 



Wood 
Iron 
Lead 



Pebble 
Pebble 



..I! 

14 
15 



wet- 
wet 
wet 



16 
12 



The little freight. 



Wood upon Pebble 
Iron upon Pebble 
Lead upon Pebble 



9 

14 

16 



wet- 
wet 



8 

8 



Upn Clay. 

For one Pound Weight with the cutting Sledge, 8 Balls. 

For the broad wooden Sledge, only 6 Balls. 

For the broad Iron Sledge, 4 Balls. 

For the cutting Iron Sledge, 5 i Balls. 

For an Ounce Weight with the broad Sledge, ig Balls. 

For the fame Weight with the cutting Sledge, 18 Balk 



CD c 2 



C O R O L 



1 96 jiCourfe '-of 'Experimental Pftikfopft^. 

C O ROLL MR T I 

The different EffeSs- of thefe Experiments will alio admit of 
a different Way of explaining them. As for example, , there is- 
proportionably more Force required to draw along, tlm little Sledge 
than the great one y and : that probably becaufe it glues it felf or 
flicks to the Parts to be overcome, and alfo the Oil or Greafe 
flicking to it become an Obftdcle, inftead of helping it as they do 
the great Weight, by filling up the Holes in the Wood or Metals, 
their Parts perhaps as they are fpherical may help as fo many 
Rollers : As Oil is not lb hard as Greafe, it does not fo much hin- 
der the little Weight, which requires. -lefs. Force to overcome, its 
Refiflance than that of the Greafe* 

GO ROLL ART W 

For this reafbn the great Weight runs more eafily over the 
greased than the oil'd Wood ; becaufe the Greafe being firmer 
Ells the Pores of the Wood better, and Keeps together the little 
Parts that rife when it is not greas'd, and which muft be broken 
or prefs'd down when there is neither Greafe nor Oil. This ob* 
liges us to employ more Force, and much more when it is wet ; 
Becaufe the Water penetrating into the Wood caufes the rough Parts 
to rife, which are like fmall Mufhrooms or Grains, of Corn that 
one muft either run over or prefs down flat. 

C ORG L L A R T III; 

And therefore when Wood is wet, as in the wooden Sledge^ 
tJiere mufl be as much again Force applied as when the Wood 
is dry ; and a Force more than double would be require if the 
Wood had been long imbibM in Water, or was of a Nature to fuck 
in a great deal of Water and to fwell upon that account 3 ; and 
though Water does not feem to be imbibM by Metals^ yet it 
is very reafonable to think from thefe Experiments that ' it does 
in fbme meafure join and glue them together ; which perhaps 
would not happen when heavy Loads are drawn by Horfes, where 

this 



M Gswje of Experim 197 

this Adhefion would hinder but little in proportion to -the greatLe£t IV* 
Weight.* v^VV) 

C O R O L L A R T W« 

As Iron fometimes appears to run more eafily over Iron than 
Brafs, and over Brafs than Copper, the Reafon leems to be, that 
Xfon being harder than Brafs it is lefs liable to yield and fink in; 
and as Copper is fofter than Bra% it finks more than Brafs, and 
confequently has more Rfefiftance and Friftion than Brafs ; as this 
appears in feveral Cafes and feveral Sledges ; and may perhaps 
do the Tame in the large ones, of which ours are but as Models. ^ 

CO ROLL A R T Vi 

We mufl not conclude from thence that Greafe or Oil fhbuld 
not be us'd in Engines, tho r here they have leenfd of little ufe, 
and fometimes have been an Hindrance, as here in the little Sledge; 
becaufe we . know them to be of ufe in great Machines, for two 
Reafons ; becaufe they fill up the Holes as we fee, or elfe rolling 
under the Weight facilitate its Motion, and they hinder the Parts 
from wearing or flying off, and befides they hinder fuch Parts as 
are broken off ; from flicking to the Work : For if large Machines^ 
as large Preffes and Screws for coining Money, were us'd without 
Greafe, they would move much harder on account of the fmall Parts 
that would wear off and flick on in other Places, and by that 
means break off more, which would not only make the Engine hard- 
er to move, but wear it out much fooner. 

C O R O L JJ A R T VI. 

But tho 5 Greafe or Oilfeems prejudicial t© fmall Machines^ 
their Motion is thereby rendered more equal; and tho' one may 
perceive the Motion to be more difficult,as in Pocket- watches when 
they are oiPd, becaufe then they generally go flower, yet then they 
go more equally : . And it is always an Advantage to have them 

* This is a plain Confequeme of the Attraction ofCoheJion; for Jince the Attraction of 
Cohefion is proportionable to the Surface or the Number of the touching Parts, and the Fric- 
tion proportionable to the Weight, the Hindrance or Lofs tf Force on account of the f aid At- 
fmttion will 'always be lefs in proportion to th* whole Frittion, as the - Weight encreafes. 



cleaned 



A Comfe of Experimental 




3^£t, W. clean'd and oil'd, for then they go better, and the Holes do ;not 
\^VNJ fo foon wear wider; the Balance plays better, and is not liable 
to vary. One might indeed ufe no Oil in fome fmall Machines 
which go eafily and are but feldom to be ^piit into Motion. 

COR O L L A R T VII. 

The Ufe of Greafe is vifible, efpecially when Wood afib^gairJft 
Wood ; for then Greafe makes the Motion as eafy again, nay two 
gds eafier if the Parts be fharp and cutting, as appear'd from the 
Experiments made with the flat and the {hasp Sledge of Wood 
drawn along on Wood not gyeas'd. 

C O R O L L A R T VIII. 

cF rckm hence alfo it appears show ttfeful Greafe is for Coach 
and Waggon Wheels; efpecially in rainy Weather; for if -the 
Naves were wet, or if there was no Greafe to hinder the Water 
from penetrating into the Wood, four times the Force would be 
requir'd to draw a Burthen, than when it is drawn with Greafe in 
dry Weather, as may be feen by the Sledge, in refpect only of the 
friction made .upon the Axektree, which is but little when com- 
«par'd with the Refinance made .upon the Ground or the Pavement ; 
but befides that Obftecle, the (Hole of the Nave would grow con- 
fiderably bigger ; for by its fwelling the Axel-tree would no long- 
er be free, and muft break offtheiPartsin its Way : Then as the 
Nave grows dry the Axel will no longer fill the Hole ; the Wheel 
will vary and be more liable to break, inthofe Jolts that happen 
as it goes over a fudden Rife or falls into a Hole. For thefe Rea- 
fbns therefore it is always well to greafe Machines. 



CO R O L L A R T 

Tho' thefe Experiments do not wholly determine every thing 
that relates to very great Weights to be drawn upon Pebbles, and 
the Motions of great Machines ; yet they fhew us which are the 
eafieft Metals for moving on one another : As alfo that there are 
Parts to be overcome or broken off in Frictions : That it is mere- 
ly the Weight and the Motion that caufe the Refiftance and Fric- 
tion, and that the Quantity of Surface does not encreafe it when 
the Parts that rub and bear do not move fwifter ; for tho' the fharp 

Sledge 




Sledge goes with more difficulty in feveral Cafes, it is pot to BeLeOt. 1% 
eonfiderM as if that way of making it would ferve to avoid or eafe vtnTO 
the Bri£tion, but as an Edge or a Saw which penetrates into the 
Body of Metals or Bodies to be cut ; and if it appears to Aide 
more eafily upon Wood, it is on account of the Grain of the Wood; 
and the Way being once mark'd it follows the Grain as in a Path, 
and then it has fewer Paths to prefs down or overcome ; but on 
Clay which has no Grain, or upon Pebbles, it goes much harder, 
becaufe the Obftacles to be remov'd are greater, as it finks more, 
wtoen fharp than when flat,, 

COR G L L A R T X. 

B y this one may fee that it is poflible to encreafe Fri&ion, by 
making the moveable Parts fo fmall that they will 1 penetrate an<f 
rub off Parts of what they bear upon, as it may happen to the 
Fivots in Watches, if they fhould be too fmall j for then they 
would loon make the Holes too big ; as likewife in Sledges* if too> 
harrow a Bar of Iron be put on, thinking thereby to leflen the 
$M&ion on the Pavement, and fo in other Cafes. 

CO R O L LA R T XL 

M e n c e may be eafily conceiv'd that tne Bottom of Sledges 
ought to be broad, and it is better to fhoo them with two broad 
Plates of Iron under each Piece, than only one narrow one ; and 
when the Streets are dry, it would be more advantageous to have 
no Iron at all, the Experiment fhewing that Wood will Hide bet- 
ter) which ftill appears more probable, becaufe the little Sledge of 
one Ounce (with its Load) Aides more eafily upon the paving 
Stones than the great one ; whereas it gjoes with more difficulty 
on other Occafions, by reafon of its being in fome meafure glued 
by its clofe Cohefion. 

C O R O L L A R T XIL 

Befides this Experiment, one may alfo infer that the Draught 
will be the eafier in dry Weather with the wooden Sledge ; be- 
cauie when Stone-duft is ftrew'd before Sledges, the Draught is 
eafier by one 4th part, whether it be upon Wood, upon Iron, or 
upon Brais : And as there are always lmall Parts rubb'd off from 



200 




Left. IV. the Stones of the Pavement by the Nails of the Wheels and the 
v*""W Horfes Shoes, befides the Duft at that time ; all which Things 
will facilitate Motion, as may be known by making a Compari- 
fon with the Experiment in which neither Stone-duft nor other 
Duft was us'd. 

CO R O L L A RT XIII. 

, As for the Iron Sledge, it is evident that it would go- moft ea- 
fily in rainy Weather ; but if it was dry Weather and the Pave- 
ment not wet, it would be worth while to try with the Sledge 
itfelf (not in Model) whether then it might not be as well not 
to wet the Pavement, as is commonly done by a little Barrel full 
of Water laid upon the Sledge with two little Holes for the Wa- 
ter to run out and wet the Pavement and the Sledge. For the' it 
is certain that if the Sledge and Pavement were lufficiently wet, 
all would go eafier ; it is very probable that it is better not to 
wet them at all, than to wet them fo imperfe&ly as only to make a 
kind of Dirt and Lumps that may prove an Hindrance. There 
would not be fo many Parts for the Iron of the Sledge to remove 
in running its Length, as was obfervd by the Experiment on the 
fmall one, which running twice over the fame Track, goes much 
more eafily the fecond time than the firft. This may alfo be ob- 
ferv'd in whetting a Knife, which Aides eafily over the Whetftone 
After having rubb'd it over once or twice when the Stone is dry, 
and fo wears but a little ; whereas it rubs hard and wears .much 
when the Stone is wet. 

COROLLART XIV. 

We don't fpeak of the Leaden Sledge ; which we only us'd 
for Curiofity , and to fhew that Parts are broken off by Friction 
and that Lead caufes moft Refiftance in many Cafes, where Pi- 
vots or Arbors are made to turn upon Lead or Pewter. 

All the foregoing Experiments are of Ufe to direct us how 
to choofe Matters or Subftances to make ufe of, and how to cal- 
culate the Force according to the Weight and the Motion which 
the rubbing Parts will have. Thofe that would try thefe Expe- 
riments over again out of Curiofity, muft take care to make them 
in the fame Order ; firft, all thofe that are dry, then thofe that 

are 



A Courje of Experimental PHlofophy. 201 



are wet, next thofe that are oil'd, and Iaftly thofe that are greas'd ;Lect IV. 
becaufe if the Machines were greas'd before they were oil'd, the l/"V"Nj 
Greafe filling up the Pores, the Effects of the Oil would only be 
like thofe of the Greafe, elpecially when we make ufe of Wood, 
which mull, after having been wet, be fuffer'd to be quite dry, 
and new plan'd again, before it be anointed with Oil or Greafe. 

Tho' I have in the Notes to my laft Lecture * mathematical * Lea. 
ly confider'd the Effects of high and low Wheels, and compar'd Ann - u - 
'em together; yet as Coaches, Waggons and Carts, and other 
Wheel-carriages are fo neceflary for the Ufes of Life, that only 
the Difufe of them for one Month would be enough to put a 
whole Nation in Confufion, I fhall here again give an account of 
fome more of M. de Camm\ Experiments and Reafbnings about 
them, being well fatisfied of the Truth he afferts from my own 
Experiments, and having found his Experiments to anfwer as near 
as can be expected in Machines that have fo much Friction as 
Models of Carts and Waggons. I have indeed a Machine with 
Brafs Wheels, whofe Steel Axes have very fmall Pivots, fo 
nicely made that any of the Wheels once fet in motion will turn 
upon their Axes for the Space of more than half an Hour, making 
feveral hundred Revolutions before they flop ; but the Ufe of my 
Machine being chiefly to fhew how near thofe kinds of Experi- 
ments may be brought to agree with a mathematical Theory ; 
we cannot expect that any Carriage to bear Weight can have fo 
little Fri£tion : f Therefore I choofe rather to relate M. de Camus ! sf Ann. ». 
Experiments made on Models of Carriages of an Inch to a Foot, 
every_ way reprefenting Carts and Waggons, and liable to as much 
Friction in proportion to this Bignefs ; becaufe it fhews us direct- 
ly what is the real Friction in the Carriages at prefent in ufe. In 
the manner of remedying Fri&ion I fhall add fome of my own 
Confiderations and Observations to his. 

I begin here with his 24 th Propofition, Sect. 5. of his Book 
above mention'd. 

Proposition XXIV. 

The Wheels of Carriages muft be exactly round, and the Fellies 
at right Angles to the Naves j according to the Inclination of 
the Spokes. 

It is a general Rule in all Cafes, that the Wheels be exaftly 
round ; for if they were not fo but like EFGHJ and the Nave >7. F. 7 . 

D d out 



s 02 A Courfe of Experimental PMIofipky, 

Le£tVIV.out of the Center; it is certain that fuch a Wheel, in turnings 
a^V^ would be affe&ed in the fame manner upon plane Ground, as other 
Wheels are when they rife and fall, and would not be in Equi- 
Lthrto ; the Wheel turning towards H would move with as much} 
difficulty, as if there was a Rife to afcend, and that Height being 
pafs'd, it would fall on the fudden as if a fquare Stone was, roll'd? 
along, and the Jolts of the Wheel would precipitate and puffi the 
Hones at one time, and immediately encreafe their Difficulty of 
drawing the next Moment ; and that in proportion to the Wheels- 
being out of round : Suppofe the Wheels to be without Angles,, 
nay truly round j yet if the Nave fhould not be in the middle,, 
*-Pl*i7.F*7-the fhorteftPart as *F being upon the Ground, when fuch a Wheel 
begins to turn the Weight muft be raisM in the fame manner as 
when another Carriage is going up an Hill, and from F to D or 
quite to G the Wheel would act like a Wedge, and at D orG 
it would fall and drive on the Horfes as in a fteep Defcent j fo that 
Horfe& or Oxen would be as much tir'd with fuch Wheels upon 
even Ground, as in {training to climb up Hill, or to bear the Shock 
of a fteep Defcent ; and this would moftly afte£fc the Tiller or 
Horfe next to the Wheels : Therefore Wheels ought to be exact- 
ly round, and the Naves and Holes of the Naves exadlly in the: 
Center of the Wheels. 

Secondly ) The Fellies muft not crofs wind, but be at right An- 
gles with the Naves according to the Inclination of the Spokes, ; 
that is, the Plane of the Circle of the Wheel, which paffes thro* 
the Fellies, muft cut the Nave at right Angles, tho'.it need not 
|>afs through the Place where the Spokes are inferted into the Nave 
for otherwife the Wheel, in turning, would find Inequalities, as it: 
happens when the Hole of the Nave is too big, and the Wheel 
moves from Side to Side, which comes to the fame as if the Wheel 
was out of round : and then the Inequality of the Spokes which 
would be too leaning or too ftrait upon the Nave descending into 
an Hole or rifing upon an Eminence oppofite to their Inclination^ 
would caufe them or the Fellies to b^eak* Therefore the Wheels 
of Carriages muft be exactly round, and the Curves of the Wheels^ 
or Fellies, at right Angles to the Naves. 

C O R 0 L L A R T I 

Hence follows, that where Wheels are not fhod with Iron 5 
great Care muft be taken to fix Wood, to the Fellies, in order to 

keep- 



A ] Courfe of ^ ExperimmalPhBofiphy. 20 



keep them round ; and that nothing is favM by ufmg no Iron ; for Lea, IV. 
if in fuch Places Wheels wear but little, becaufe they only go upon vYV 
Earth, it would only be making the Iron Plates thin, which would 
then coft but little ; and that Expence once over, the Wheels 
would be preferv'd longer and more Work would be done, fo as 
to make the Gain far exceed the Expence. Whereas in Countries 
where they do not llioe Wheels with Iron or fecure them with 
Wood, the Wheels wear fo as at laft to be rather fquare than 
round, and thereby the Horfes or Oxen being very much fatigued, 
hardly do half the Work that they would do if the Wheels were 
kept to their Roundnefs. 

Proposition XXV. 

The Spokes maft be inclined to the Naves y that the Wheels 
may be difhtng, or concave. 

If Wheels always turn'd upon fmooth and even Ground, it is 
certain^ that, the Spokes ought to be ftrait upon the Naves, that 
is, at right Angles to their Axes ; becaufe then they would bear 
perpendicularly, like the Spokes B of the Nave AC,* which is*PLi7.F,8 t 
the ftrongeft Way for Wood : But becaufe the Ground is unequal, 
and when the Wheels fall into the Ruts, that Wheel which is 
in the Rut bears a greater part of the Weight than the other, 
becaufe it is lower (as we have demonftrated it) in fuch a 
Cafe, the Spokes of a difhing Wheel become perpendicular in the 
Rut, and therefore have the greateft Strength ; whilft the oppofite 
Wheel being upon higher Ground bears a lefs part of the Weight, 
and confequently the Spokes need not be at their full Strength* 
and fo will have a fufficient Force tho* that Force be lefs than 
what they have upon even Ground. The Spokes therefore ought 
to be inclined, to make the Wheel difhing as is the ufual Pra&ice* 

P R O P O SIT I O N XXVI. 

The Axel-trees mufl be Jlretght In all refj?e£ls^ and at right 
Angles to the Shafts or to the Tote. 

In the Motion of all Bodies, there is one Way of moving, 
which is the eafiefl: of all the reft \ and that happens here when the 
Axel- tree is every way ftreight. For if its Ends fliould bend back- 

D d 2 ward. 



204 A [ Cmrfe of Experimental PMIofophy. 



Left IV. ward, fo as to bring the Wheels nearer together behind as A E** 

^[Y^y m ^ *P reac * them much before as DC, it is certain that they could 
7 ' ' 9 not go into the Ruts nor turn in going forward, or at leaft with 
great difficulty, dragging kftead of rolling : There would be the 
lame Inconveniencies in bending the Axel-tree forward, fo as to 

+p].i7,F.io.bring them nearer the Pole as IF,f and make them fpread behind 
as at BD. The lefs the Axel is bent, the lefsthe Inconveniency j 
but there will always be fome, when the Wheels are not parallel^ 
therefore the Axel ought not to be bent at all. 

H Fig. 9. I F t h e Wheels fpread outwards as D C || , or inwards as I F, 
there will ftill be three other Inconveniencies. If the Axel bpnds 

* Fig. iq. outwards fo that D C * bears upon the Ground, the Way will be 

too wide ; it will be hard to turn ; and the Weight being drawn 
t Fig. 9. forward will crufh the Wheel, the Length of the Spoke CHf ia 
that Cafe a&ing as the Arm of a Leaver to break the Axel or the 
Spokes, C being the long Arm,, the Center of Motion at one End 
of the Nave, and the fhort Arm at the other. If the Axel be fo 

* Fig. 10. bent as to bring the Wheels inwards as at I and F,* the fame three 

Inconveniencies would happen ; the Way would be too narrow* 
and the Weight would tend to crufh the Wheels, and there would 
be a Difficulty in turning : Befides, they would bear but on the 
Edge of the Iron and become cutting by their fmall bearing.. 
Therefore as fuch Inconveniencies will happen more or lefs ac- 
cording to the bending of the Axel; it fhould not be bent at alt 
But there will be no Inconveniency when the Axel is ftreight and 

I Fig. iu the Wheels are in the Situation OP, AD. f By this means the 

Wheels will have Liberty as they go along ; but otherwife, tho' 
a Wheel when off of the Ground might turn upon the Axel, yet 

II Fig. 9. when on the Ground and drawn at H||, it would only drag. 

The Axel muft alfo be at right Angles, to the Pole or Shaft. ; 
for if the Pole or Shafts were on one fide as at B, the Coach or 
Carriage would be drawn on one fide, and almoft all the Weight 
Would bear upon one Horfe ; but it muft be at right Angles like 
> Fig. 11. the Pole G,* as has been faid before. Therefore the Axel-trees of 
all Carriages muft be ftreight, and at right Angles to the Pole or 
Shafts* 



C O R O L L A R T I. 

This fhews the Inconveniency of thofe Coaches, whofe Axels 
are bent fo as to make the Wheels fpread upwards that they may not 

touch 



A Com fe of Experimental Phihfophy. 20 



touch the Braces ; for this brings on all the Inconveniencies above lied. iVi 
mention'd, and the Coaches are more liable to turn over, becaufe w^v*sj 
the Way is narrow'd, and they go into the Coach-houfes with 
more difficulty fpreading at top, the Tops of the Wheels being 
more afunder than if the Axel was ftreight, and when they ftrike 
againft any thing at top, they are more liable to break ; and then 
likewife the rolling of the Wheels is hinder'd ; therefore it would 
be better to bring in the Braces nearer together, or let the up- 
right Wheels further afunder. 

COROLLART III, 

This Way of bending the Axel does alfo render ufelefs the 
Advantage gain'd by difliing the Wheels, as has been explain'd : 
for in this < Cafe the Spokes of both Wheels bear perpendicularly at 
the fame time as if they had not been inclin'd to the Nave ; and 
when a Wheel comes into an Hole or deep Rut, the Spokes being 
no longer perpendicular, it is more liable to be crufh'd by the 
Weight. This makes the Wheels and Axel-trees more fubjecl to 
break, and the Spokes to be loofe or break. Nay, in even Ground 
they cut more, and bear on the Edge of the Iron Plate, as one 
may obferve in fuch Wheels that the fhoeing is more worn out-, 
wardly than inwardly ; and this occafions their Aiding the more 
upon paved Streets. 



Proposition XXVII. 

The Hind-wheels do not drive or imfell the Fore-wheels ; iet 
the Hind-wheels be ever fo high, and the Fore-wheels ever 
fo low. 

I n fome of the Ancients Pictures one may fee Chariots repre- 
fented with four Wheels all high and equal. In fome Countries, 
where Fafhions feldom change, they ftill retain thofe forts of 
Wheels. People, in all probability, lowerM the Fore-wheels in 
order to turn the more eafily becaufe of the Shafts being in the 
Way. The Fore-wheels have alfo been lower d frill more in Coa- 
ches by reafon of the Braces which in fome meafure hinder the 
turning fliort, and are liable to be cut by the Wheels : Afterwards 
Crane-necks have been invented for turning yet fhorter, and by 
degrees the Wheels made low enough to go quite under the Bend 



2o6 A Courfe of Experimental Phtiofb 



Led. IT. of the Crane-neck, Then feveral Coachmen pretend that their 
i/V>J Horfes tire becaufe the Fore-wheels are too high, fo as not to be 
driven on enough by the Hind- wheels :. And this falfe Principle 
has been followed even to Childrens Carts and Toys which are 
made with very low Wheels before. It is very likely that they 
would be made ftill lower, if it was not evident that by making 
them a little lower they would not go at all over fome Rubs, nor 
get out of deep Ruts. Coachmen generally encourage lowering 
the Wheels, not only becaufe of the eafy turning, and their Ima- 
gination that the Hind wheels drive on the Fore-wheels if they be 
much fmaller; but chiefly becaufe of their getting up eafily into 
the Box. Now if the Fore- wheels are upon fmooth and even 
Ground, we fhall find that the Fore- wheels will be at reft tho'ever 
fo low, the Center of Gravity of each pair of Wheels being fo 
placM that the Line of Direction falls between the Wheels both 
in the Fore and Hind- wheels. Therefore the Carriage cannot 
move of it felf in that Situation, only the Fore- wheels are more 
loaded becaufe they are lower than the Hind- wheels; but it does 
not follow from that, that they roll more eafily ; for if it was fo, 
Carriages would be more apt to roll when moft loaded, which is 
contrary to Experience . A Confequence alfo of this Principle of 
Wheels driving would make a Carriage with very high Hind- 
wheels and low Fore-wheels go of it felf upon even Ground, which 
never was j therefore the Principle is falfe. 

$ C H O L I V M. ■ 

If the Hind-wheels could, by their greater Height, drive the 
Fore ones, it would follow that a Coach or Carriage would go 
with moft difficulty when the high Wheels go foremoft by ma- 
king the Horfes draw behind. Now let a Carriage be made in 
Model with Hind- wheels of five Inches, and Fore- wheels of two 
Inches and three Lines, which is the common Size, if we take an 
Inch for a Foot (tho' fome Hind as well as Fore- wheels are lefs in 
Proportion) and let this Carriage or Waggon be fet upon a fmooth 
Board, and loaded in the middle with five Pound Weight of Lead ; 
let a fmall Pulley be fix'd at the End of the Board, over which 
runs a filken Thread faften'd at one End to the Waggon and at the 
other to a Scale, or a little Linen Bag to receive Leaden Balls to 
draw the Loaded Waggon by their Weight. The fame Weight 
that draws the Waggon with the fmall Wheels foremoft, will alfo 

draw 




#aw it with the great Wheels foremoft, provided the Line of Left; IV. 
Direction of the Draught be in the fame Situation in both Cafes : v/y>o 
This fhews that there is no driving whatever Difference of Height 
there be m the Wheels, even upon plane, horizontal and fmooth 
Ground- 

C O R O L LA R 1 I. 

It follows that this Notion oi driving muft have been from; 
feme Workmen who thought the Ca^e to be parallel between a 
Carriage upon an inclmM Plane, and one with high Hind- wheels 
and low Fore- wheels, tho' on an horizontal Plane ; but the Cafe 
is very different, for on an inclined Plane the Line of Dire£tion 
falls out of the Bafe, and the /Equilibrium is loft ; therefore 
the Carriage will roll till it finds it or meets ^with fome Obfta- 
ele that reduces it to m /Equilibrium* This would do the 
iame in one or two Wheels as well as in four, if one Wheel was 
broad enough to fupport it felf. If this be calPd driving y a Cart, 
tho r it has but two Wheels, will have it as well as a Coach on 
Waggon. 

CO R O L L A R T II 

I t is not a good Obje£Hon to fay, that the great Wheel being 
in Motion continues to move longer than the ftnall Wheel, and lb 
drives it \ for upon the Ground the Refiftanee is much greater than 
fuch an Impulfion.. For if we give by Force fome Degree of Ve- 
locity to a Waggon on plane Ground, but fuch as may let it fink; 
m ever fo little, as in wet Weather or upon foft Ground, not fa 
hard as Pavement, as foon as the Force ceafes to a£b, the Waggon 
will ftand quite ft ill,, which fhews the Hind- wheels do not driva 
even in that Cafe. 

COR O L L A R T HE 

If we confider the Thing upon a Pavement, be it even or un- 
even, or upon rough Ground with Rifes and Falls ; let the Wag- 
gon be fo placM as to have the high Wheels upon the higher 
Ground, then indeed the Waggon will run down, and they will 
feem to drive the low Wheels ; but then in rifing again, the Fore- 
wheels will driva the Hind ones, and the Waggon will run back- 
wards : 




2o8 A Courje of Experimental 

Left. IV. wards : To fay that the great Wheels turning more eafily will 
wv-^ drive the better, only Ihews that the Waggon will go better if 
all the Wheels are large, and that they will altogether roil better 
than if there were two little Wheels. So that little Wheels before 
do not (whatever Way you confider them) facilitate the Motion 
of a Carriage* 

Proposition XXVIIL 

Great Wheels are always more advantageous for rolling than 
little ones, in any Cafe or upon any Ground whatever. 

The Wheels of Carriages are confider'd according to the Ve- ; 
locity and F iftion they have upon the Axel-tree, and likewife ac- 
cording to their Refiftance or Sinking in upon the Ground. If we 
confider them according to the Fri&ion, it is certain that a Wheel, 
whofe Diameter is double, that of another, will make but one Turn, 
whilft the little one makes two, for the fame Length of Way, the 
Circumference (which is in proportion to the Diameter) being 
double : Therefore in refpe£t to Fri&ion, a Wheel of double the 
Diameter will have a double Advantage, there being but one Turn 
inftead of two, which doubles the Fri&ion in the fmall Wheel 
*H.i7.F.i2,The Wheel ABC* being twice as big as the Wheel DEF, will 
and I?e have twice the Advantage in refpe£t of the Fri&ion, the Holes of 
the Naves and the Axels being equal. 

If we confider the Wheels according as they fink into the Earth 
or fall into Holes, there will be the fame Advantage for the 
one and Inconveniency for the other : If we confider the bearing, 
it is double in the great Wheel, therefore it will fink but half the 
Way ; and if we confider Hollows, it will give the fame Advan- 
tage in fome Cafes ; but then in others (as for example, where 
the Holes are deep) the little Wheel will have much more Difad- 
fL. 3. Ann. vantage ;f for if it fhould fall into a great Hole as DE,j| of a 

HFi^ig. 3 ' Diameter equal to that of the Wheel, it would wholly fink in, 
whilft the great Wheel would only fall in the Depth of its Seg- 
* Fig. 12. ment AB, * which would not be half the Wlieel, as is eafy to 
f F.ia& 13.be underftood by the two parallel Lines A D and B E : f We may 
^uppofe the fame to happen in marfhy Grounds where the little 
Wheel would fink Wholly in the lame Hole that the great one 
would fink but in part* 



If 



A Courfe * of Experimental Philofophy. 209 

If we confider an Eminence to go over upon even Ground as Left. IV. 
a Pavement, and that it is the fame at B as it is at E, * the Seg- 
ment or the Chord of the little Wheel will be one 3d nearer the 
Top than the Segment or the Chord of the great one, and there 
muft be a third more Force to overcome the Rub. If the Rub be 
fomething which muft be broken or crufh'd, wholly or in part, 
there will be the fame Proportion and the Circumference of the 
Wheel making a fort of Wedge or inclin'd Plain, it will be fhort- 
er or lefs acute in the fmall than in the great Wheel, fo that the 
Effort muft be greater to overcome it all at once. And if the 
Rubs are only Rifes and Falls of Ground, there will, for the fame 
Reafon, be more Difficulty for the little than the great Wheel. 
Confequently great Wheels are better for rolling than little ones 
on any Occafion or upon any Ground whatfoever. 

CO R 0 L L A R Y I. 

Hence it follows that if a Wheel be only one Inch in Dia- 
meter, or in Height, more than another, it will have more Ad- 
vantage^ and that the higher Wheels are, the more advantageous 
they are in proportion, provided they are not too high, that is, 
not above five or fix Foot high ; for if they fhould exceed that 
Proportion, they would themfelves become a great Weight, or if 
made light, then they would be too weak and fubjecl: to break on 
account of the great Length of the Spokes ; befides, with fuch 
Wheels Horfes would be hinder'd from exerting their utmoft 
Strength by having the Axel-tree higher than their Breaft ; fo 
that they would draw downwards, efpecially if the Horfes are not 
very tall ; as in little Wheels the Draught is made more difficult 
by the Horfes drawing upwards : For to deviate from an horizon- 
tal Line of Direction by drawing either upwards or downwards, 
is inconvenient for the Horfes, as will appear more plainly by the 
following Experiments. 



Proposition XXIX. 

C ARRl A GES with four Wheels as Waggons or Coaches 
are much more advantageous than Carriages with two Wheels ^ 
as Carts and Chaifes. 

E e What 



2 1 o A Coitrfe of Experimmtd Thttajbffiy. 

Le£fc. IV. What we are to confider in Carriages is the Advantage whidfe 
l/V'V they have one more than another in rolling, and the manner of 
applying Horfes or Oxen in fuch a way as they may be the leaffc 
fubje£t to tire, and that they may draw with the greateft Advan- 
tage. Now in applying Horfes to a Cart with two Wheels, it is 
plain that the Tiller carries part of the Weight in what manner 
f oever the Weight is in JEquilihrio upon the Axel ; for in going 
down an Hill the Weight bears upon the Horfe, and in going, 
up Hill the Weight falls the other Way and lifts the Horfe ( that 
is, pulls him upwards) which takes away great part of his Force j v 
and if to avoid this laft Inconveniency, the worft of the two,, the 
Weight be put forward, the Horfe will the fooner tire for carrying, 
%s well as drawing : Befides, as in the Holes in the Road fome^ 
times one Wheel finks in and fome,times ; another, the Shafts ftrike 
againft the Tiller's Flanks, which is the Deftrufltion of many 
Horfes. 

Moreover as in a Cart the whole Weight bears intirely up- 
on two Wheels, when one of them finks into an Hole or Rut* 
half the Weight falls that Way, and to draw the Wheel out of the 
Hole, half the Weight mud be drawn out ; if it be upon foft 
Ground, where both the Wheels fink in and muft be drawn out^ 
the Labour is greater than when the four Wheels of a Waggon 
fink upon the fame Ground, becaufe the Weight being diftribu- 
ted upon four Wheels muft make them fink lefs than if it was on- 
ly fupported by two \ and in Holes where one Wheel only finks 
in at a time, there is only a quarter of the Weight to be drawn 
out, but half when we ufe the Cart, in which cafe therefore a dou~i 
ble Force muft be us'd to draw out half the Weight : If two Wheels; 
of a Waggon fall at once into an Hole, then only half the Weight 
is to be drawn out, but the whole Weight when we ufe the Cart ; 
and in the ' Rifes and Falls upon Pavement, as in croffing a Ken- 
nel in a Waggon, an Mqmlibrium is oftenf made between the Hindi 
and Fore wheels, thole in coming down heJpijQg thefe to rife as, 
they are juft got over the Kennel ; and if this happens only on 
one fide, there will be the fame Help ; but in a Cart it would- 
happen otherwife, for one of the Shafts would ftrike the Tiller in 
the Flank. As for the Objection, that there is lefs Friffcion upon 
two Wheels than four (which very likely has been the Reafon for 
preferring Carts to Waggons} it is wholly falfe, for we have fhewny 
that there is as much Fri£tion upon two Wheels as upon Four, if 
there be the fame fk'd Hole in, the Nave 5 and the Weight be the 

J^aiidQo 



A Courfe of Experimental PMqJhphy. 2 1 1 



^fama On the contrary, there will be rather mere in the Ufe of Led. IV. 
the Cart ; becaufe as all the Weight bears upon two Points the i/Y^ 
fmall Parts will be more liable to be torn off, the wearing being 
double ; and if the Load on the Waggon be not greater than on 
the Cart, by making the Axels and Holes of the Naves lefs, it will 
liave ftill lels Fri&ion ; but the Fri&ion (or at leaft that Difference 
of it) being but little when the Wheels are well greas'd, it is not 
worth Notice. Belides, the Advantage ffaewn in the Ufe of four 
Wheels, we muft have Regard to the Till-Horfes which carry as 
well as draw in the Cart, but in the Waggon exert more Strength 
to draw, and yet laft longer becaufe they are not bangM on the 
Sides . Therefore four-wheePd Carriages, as Coaches and Wag- 
gons, are more advantageous than Carts and Chaifes* 

Proposition XXX. 

IT would be much more advantageous to make the four Wheels 
of a Coach or Waggon large and nearly of a Height, than to 
make the Fore-wheels of only half the Diameter of the Hind* 
wheels j as is^ujual in many C P laces. 

I f there be fome Conveniency for turning in making the Fore* 
wheels of Coaches or Waggons as little again as the Hind-wheels, 
there is a very great Difadvantage, becaufe half the Force is loft 
that would be effe&ual if they were large, according to the 26th 
Propofition, The Jolts alfo are greater when we ufe little Wheels, 
becaufe they fink as low again in the Holes and Hollows of the 
Pavement, and therefore muft jump as high again ; and this, no 
doubt, has brought People to contrive Springs to avoid the jolting, 
but at the fame time it has made Coaches more apt to overthrow 
by railing the Body of the Coach the higher to place the Springs 
under it. 

Besides thefe Difadvantages, Horfes that draw upwards tire 
fooner and grow more ftiff in the Hams ; and this is the Reafon 
that Horfes that have been usM to a Coach are no longer fit to 
be ridden, tiring their Riders very much, which would not happen 
if the Fore- wheels were high, and the Points where the Traces 
are fixM were as high as their Breaft, fo as to. draw in Lines pa- 
rallel to the Ground, as Cart-horfes commonly do, and thereby gain 
fo much as to overcome the Difadvantages that Carts otherwifc 
have, 

E e 2 This 



212 A Courfe of Experimental PMlqfo 



Left. IV. This Advantage of Carts would ceafe if the four Wheels of 
t/V>J a Waggon were equal, and then one would have the above-men- 
tion'd Advantages alfo of four Wheels over two. Some objeft^ 
that the Horfes drawing upwards lift the Coaches out of the Dirt 
and eafe the Weight ; but if they do, then they carry a Part of 
the Weight ; and as Horfes one with another are able to carry but 
2 co ft , but can draw near iooo ib on a Waggon, this Way mull 
tire them more than fair drawing when the Traces are parallel to 
the Ground ; therefore it is befl: to have all the Wheels of a Coach 
high and equal, &c. 

$ C H O L I V M. * 

The following Experiments will confirm what I have been 
explaining. Let us make ufe of a little Waggon or Model of 
an Inch to a Foot reprefented in the feventeenth Figure of the 
feyenteenth Plate, with the four Wheels of five Inches and nine 
Lines, and fo contrived that one may put on Wheels of diffe- 
rent Diameters; as for example, Four of 5 Inches, .Two of 
0 Inches 3 Lines, Two others of 9 Inches, and let them have 
Naves, Spokes, and Fellies in proportion, to reprefent the Wheels 
of a Coach or Waggon. Let them be changed one after another, 
*Pl.i7.F. 17, the. Waggon ^ DB being always loaded with the fame Weight A 
of % ib, and drawn by means of a filken Thread running over a 
Pulley, with a little Bag or Scale of a Balance to put in Balls for 
the different Wheels, according as they are to run on even Ground 
upon Earth, Sand, or Pavement. The Board AF muft be of Oak, 
three Foot long, plan'd on one Side, and carv'd on the other to 
imitate the Pavements and the Kennels of Streets : The paving 
Stones muft: be of 7 or 8 Lines inftead of 7 or 8 Inches, reducing 
them from Inches to Lines, as the Wheels are reduced from Feet to 
Inches. It muft be fo contrived, that the Pulley may be turned to 
either Side of the Board. The whole being fo difpos'd, the Expe- 
riments will anfwer to the following Table. 

To reprefent a Cart we hang in jEquilibrio under an Axel- 
tree, the fame Weight A of 5 tb, and a Pole only is made faft 
to the Axel-tree to tye the String to it, which makes the Cart three 
times lighter than the Waggon in making the Experiments ; for 
the Waggon has an Axel-tree and two Wheels and Shafts more 
than the Cart ; and the full Wheels of 5 Inches and 9 Lines weigh 
twice as much as the Five-inch Wheels with Spokes. 



A Ottrfi of Experimmtd PhUqJbphy^ 21 j- 

To draw the Load of 5 flb upon the finooth Side of the --Board Eeft-.W 
laid level with the four great Wheels, each of 5 Inches 9 Lines in 
Diameter, there is occafion but for three quarters of a Ball 

For the Weight of Five Pounds upn the Waggon^ 



With the Four Wheels of Five Inches 
With the Two little Wheels before 



Balls 



With the Wheels of Three Inches before 



For the Cart- and the fame Weight, 



With the Wheels of Five Inches — — - — 2 

With the Two little Wheels — — — g 

With the Two Wheels of Three Inches — 3 

With the Waggon upon very moift Ecwth. 

With the Four biggeft Wheels, 2 Lines wide or thick 12 

With the lame narrower and almoft cutting — — 1 6 

With the Four of Five Inches, Three Lines wide 6 

With the Two leafl: before — — — ■ — — ■ : ;. .., , :■ 12 
With the Two of Three Inches before. 



For the Cart upn the fame Earth. 

With the Two great Wheels — — — — ■ p | 

With the Two leafl: - — ~- — — 18" 

With the Two of Three Inches ^— ■ , -.^ 1 3 

For the Waggon upn d?y ; {LaMd^ 

With the Four Wfoeelslof Five Inches ■ l , ^ 28 

With the leafl: Wheels before ~ ■— — ~ — — 46 

With the Wheels of Three Inches before.- ~— - 35 



For 




214 Qwrp § .m§mm$^ 




For the Cart upn dry Sand. 

"With the Two Wheels of Five Inches — - — * 40 

' When it flopped with 39 Balls, T was obli£d to add .1© 
^<?r£ to make it move from that Stop. 

For the Waggon ujpon wet Sand. 

With the Four Wheels of Five Inches — - 14 

With the Two leafl: Wheels before — < — — - 28 

With the Wheels of Three Inches before - 17 

For the Cart upon wet Sand. 

With the Two Wheels of Five Inches — — - 1 7 
With the Two Wheels of Three Inches — — — » 24 

7*o overcame an Eminence or Rub of Two Lines r for the 

JVazson. 

With the Four Wheels of Five Inches > - ■ - - ■ 20 
With the Two leafl: Wheels before - ■' - • - go 
With the Wheels of Three Inches before ■ 1 .■■ 25 

Half the Number of Balls will do when only one Wheel 
goes over the Rub. 

For the Cart to go over the fame Rub. 

With the Two Wheels of Five Inches . — -- 3 5 

With the Two leafl: Wheels — -— — 60 

With the Two Wheels of Three Inches. ■ . 48 

For the ffiaggm to overcome an Height of one Urn. 

"With the Four Wheels of Five Inches — — 15 

With the Two leafl: Wheels before - — — 21 

With the Two Wheels of Three Inches before — 17 

tor 




215 

For the Cart to mo over tie fame RuK vyv 



With the Two Wheels of Five Inches — - — — - 27 
With the Two leaft Wheels — — — g-8 
With the Two Wheels of Three Inches ~ * 31 

For the Waggon to come out of a Hole y m if.a gaving. Stom 

"was wanting under each Wheel* 

With the Four Wheels of Five Inches » — > g 



With the Two leaft Wheels before — — 1 

With the Two Wheels of Three Inches — — 1^ 
If the Weight be laid upon the little Wheels before, \ 

to come out of the fame Hole, we mufl: put in j 34 
But if it be laid upon the Hind- wheels and the! 
Ground even, only . j 3 

For the Cart to he drawn out of the fame Hde^ 

With the Two Wheels of Five Inches — — 18 

"With the Two leaft Wheels — — — - 34 

With the Two Wheels of Three Inches — — 25 

For the Waggon to be drawn from an Hole, as out of th 

Channel or Kennel of the Pavement. 

With the Four Wheels of Five. Inches 41 

W ith the Two leaft W heels before «~~-~_ — — — . g 
With thofe of Three Inches — . ^1 

For drawing the Cart out of the fame Hole. 

With the Two Wheels of Five Inches — - — — iq, 

With the Two leaft Wheels — . . — «. 

With the Two of Three Inches ™ ■ ^ ij ; 




2 1 6 ji^Q Philofbphj. 

Left. IV. 

v-^-v-s-. For the Waggon upon the Pavement. 

Balls 

-With the Four Wheels of Five Inches ■ • 2 | 

With the Two leail: Wheels before — — — - 43. 

With the Wheels of ^hree Inches — — _ 3 | 

When the Wheels of Three , Inches are behind, and 1 L 

thole of Two before — — S 4 2 

For the Cart upn the Pavement. 

With the Two Wheels of Five Inches — 4 X 

With the Two leaft Wheels — — — g z 

With the Two Wheels of Three Inches — 6 1 

If the Board be raised an Inch at the End where the TuUey ts^ 

For the Waggon. 

"With the Four Wheels of Five Inches — 4 1 

With the Two leaft Wheels before — — — 6 ± 

With the Two Wheels of Three Inches before 5 f 

For the Cart in the Fame manner. 

With the Two Wheels of Five Inches — s 

With the Two leaft Wheels — - — — — x 1 

With the Two of Three Inches — . — . 8 

If. we make ufe of the Four great Wheels of Five Inches and 
nine Lines, about one quarter more of Force is requir'd than for 
the Wheels of Five Inches which are three Lines wide, and that as 
well for the Waggon as the Cart ; becaufe as thofe largelt are ve- 
ry narrow and almoft cutting, they run into the Separations of the 
Pavement, and after Aiding down between Two pavements, to rife 
up again there is more Force requir'd, and they go lefs fwift than 
the broad Wheels, even when that Quarter of Force is fuperadded 
and tho' they are fo much bigger ; but upon plane and fmooth 
Ground, where they don't fink in, they go much eafier, and have 
more Advantage than the others. 

CO RO L- 



A Courfe of Experimental 'Philofophy. 217 

Left. IV. 

COROLLART I. 

Whence it is eafy to judge how much thole Carters are de- 
ceiv'd who would have the Irons or Shooings of the Wheels to be 
made very narrow, that they may the better come out of the Ruts, 
and cut the Ground the more eafily : For if the Wheels have no Fric- 
tion on the Sides of the Fellies, being narrow they fink deeper and 
fpoil the Ruts the more ; and if they go where there are no Ruts, as 
on Earth, they will tire the Horfes much more, one fourth part more 
Force being requir'd. Such kind of Wheels are very difadvantage- 
ous to every Body, becaufe they cut the Ruts the deeper. 



COROLLART II. 

T h e fame Inconvenience happens upon Pavement, and the Irons 
of the Wheels being narrow they wear out the fafter, bearing in 
fome meafure but upon one Point ; and as the Iron Plates wear, 
they grow round, and Aide more ftrongly between the Pavement, 
which alfo breaks them eafier than thofe that are wider. 

CO ROLL ART III. 

B y the Experiments upon the fmooth Board, it appears that the 
Friaion upon die Axel-trees is inconfiderable ; for with the Wag- 
gon that had the four Wheels of five Inches and nine Lines, one Ball, 
twenty of which weigh a Pound, draws a Weight of fix Pounds, 
or a Weight of five Pounds, with the Wheels of five Inches: The 
Waggon together with the Wheels weighing befides, about one 
Pound and a quarter, which makes the whole Weight taken toge- 
ther, equal to f 90 Balls. So that in this Cafe, one Pound would 
draw 1 90 Pounds ; or, what amounts to the fame thing, the Fricti- 
on on the Axel would be only equal to the 190th part of the Force 
with Wheels in this Proportion. * For when the Ground is perfect- * Am,. 4 
ly even, all the Refiftance arifes from the Friaion, which is but 
{mall in comparifon with the finking in of the Wheels in Earth and 
Holes, from whence they muft be raifed. 



COR OL 



21 



A Courfi of ■.^jerimental \BhUoJh^hy. 



Led. 1%. 

<S>rs* q 0 R O L LA R T IV. 

B y the Experiment of the Cart whofe Weig|it; bears only upon 
two Wheels, it appears that the Fri6tion is double when compared 
with that of the Waggon withibur Wh^ 

double the "Weight for the Cart, and even then it does not go till 
it be, put , into Motion,, whereas the Waggon goes of itfelf ; and 
double the Weight, or thereabouts^ is required for Wheels, of half 
the Bignels. This perhaps, ii not altogether owing to the Fri&ion, 
for it ought to be, double in the little Wlieels compared with the 
great ones, fince they go twice round while the great ones go but 
once round ; and tho v the little Wheels in the Cart muft be fet a 
going as well as the great ones, yet they go a little fafter than the 
two great ones, and the two great ones in the Cart fafter than in 
the Waggon, tho' they move in zigzag : This may alfo partly be 
owing to their not being perfectly round, nor in aquUibrio upon 
the Axel, which is not fenfible in the Waggon: And this fhews 
that it is a great Difad vantage tq make ufe of Carts, even, in re« 
fped of Friaion. 

COR O L LART V. 

It is eafy to conceive, from the Experiments made upon hard 
Clay and upon Sand, that half the Force is generally loft in a Waggon 
when little W heels are before inftead of great ones ; for tho' it does 
not appear that half is loft upon the Ground when the Earth is firm, 
there would be much more than half loft, if the Earth was foft, as 
we fee more is loft on dry Land. Befiides, one would often be 
mir'd with little Wheels in thofe Places where great ones would go 
through. 

C O RO L LA i? r VI. 

And tho' half the Force be not loft upon the Pavement, efpecially 
when a Waggon or Coach is drawn by the Horfes in a Trot, becaule 
as the Wheel goes down the Declivity of onq Pavement, it acquires 
a Force to rife up the next ; but yet if we obferve the Horfes draw- 
ing, we fliall fee that they grow heavy or ftiff in the Hams draw- 
ing upwards, and on that account in thefe Circumftances we may 
alfo reckon half the Force even upon a Pavement j bat there will 
be more loft on Riff Clav and Sand. C O- 




COR O L L A R T VIL u'SrSj 

I f we add to this the Cohfideration of the hinder Axel being 
bent in a Coach, which makes the Wheels be lefs free, we need not 
wonder that vigorous Cbach-Horfes^ that are well look'd after, will 
be fatiguM when they have drawn two or three Hours in theStreets* 
and have gone four or five Miles upon the Pavement : And for the 
Country we muft ufe four or fix Horfes, and we find that if they 
be back'd a few^ Steps they'll be out of Breath, by reafon that the 
End of the Pole is low, and has a Tendency to break in fuch a low 
Direction ; whereas the Force and Dire£Hon would be wholly em- 
ployed in going forward or backward, if the Pole was as high as the 
Breaft of the Horfes, by having high Wheels before. 

CO R O L LA R T VIII. 

He kce we may find that Horfes pay very dear for the Conve- 
ijiency of a fhort Turn, and that it would be better to go to the 
End of a Street for the Conveniency of turning ; for fince half the 
Streets are inconvenient even for a fliort Turn, what would it fig- 
tiiFy if the Wheels were high, and the Pole had not the Crane- 
iieek or archM Piece behind^ to go a little farther, or croft a few 
more Streets ? It would be better for the Horfes, and even for the 
Coachmen, who would be lefs fatigu'd with the Jolts, and that 
would be fufficient amends for a little more Trouble to get up into 
their Boxes, which happens but once, whereas they are Ihak'dwith 
a thouland Jolts. Their Mafters would be lefs interrupted in their 
Bufioels, by fuch jolts as happen in the fliort Turns, and the Coach 
itfelf would be lefs liable to overthrown 

C O R C L L A R T IX, 

Therefore the Contrivance of a circular Piece or Crane- 
neck for turning, which obliges one to have little Wheels, has much 
more Incoveniency than Ufefulnefs, both for the Horfes and Coach- 
men, befides the greater Expence of the Crane-necks and the 
Springs, which are often the occafion of overtiming by raifing up 
the Goach too high, as has been faid. 



V f 2 



C 0 R 0 L- 



22o A Courfe of Experimental Philofophy. 

Left. iv. 

{y ^ rsJ C O R O L LA R T X. 

Considering thefe Experiments made with great and Jit- 
tle Wheels, it is not hard to conceive that the Berlins are harder 
for the Horfes than Coaches; befides the Lownefs of the Fore- 
Wheels, the Shafts do not yield, and the Pole that bends fends 
back the Wheel a little when there is a Rub to be overcome, and 
then draws it on more fwiftly ; this makes the Wheel ad back- 
wards like a Wedge : If Berlins are left fubjed to overfet, when 
they do, the Fall is the greater: If they coft lefs, the Wheels muft 
be oftner repair'd, becaufe in the Berlins the Wheels cannot have 
long Naves ; and then the Shafts break oftner than Poles. 

C ' 0 R O L L A R T XI. 

Tho' it may feem that there is not fo much Advantage in go- 
ing up and down for great Wheels as for little ones, becaufe as 
they roll eafily they are troublefome to the Horfes when they are 
going down, and that the little ones not rolling fo eafily are not fo 
difficult to ftop ; and befides, that in going up Hill, the Fore- Wheels 
are not fo much loaded, and therefore lefs Force is requir'd in pro- 
portion to the great ones than upon plain Ground : Yet it appears 
that in going up there is always more Force requir'd for little 
Wheels than for great ones, and that it will always be fo propor- 
tionably ; for as the Diredion is lower, the Horfes are thereby 
more tired, and tho' the great Wheels are more rolling, the Horfes 
too have the full Advantage of their Strength to flop them, the Pole 
being then Breaft high, whereas it is very low when we ufe fmall 
Wheels, and it tends to break, as often happens in going down 
Hill : So that all being well weigh'd, there is at leafl: as much Ad- 
vantage in proportion for the great Wheels as the little ones in go- 
ing up and down Hill: Befides, in travelling we go an hundred 
Steps upon plain Ground for one up or down Hill 

COR O L L A R T XII. 

There is another Difadvantage for little Wheels, which is 
that they break the Pavements and fpoil the Ways more than <*reat 
ones : Befides, they bear more Weight, and having lefs Bearin^thev 
link deeper and jump up higher; which hurts the Houfes which they 

fhake 



A Courfe of Experimental Philofophy. 22 1 

fliake as they go by ; they make more Noife and alfo fplafhLeft.lV 
more. 

C O R 0 L L A R T XIIL 

One may fee the Difference of ftiff Clay, Sand and Pavement, 
that it is always moft advantageous to draw on the Pavement, and 
that Horfes muft needs tire very much on Sand ; but that in Rainy 
Weather it is often better to go on the Sands than the common Earth 
when it is a ftiff Clay, But in dry Weather Earth is better than 
Sand, Sand being more eafy to draw upon when Earth is the moft 
difficult, &r. 

C O R O L L A RT XIV. 

According to the Experiment of bringing forward the 
Weight upon the little Wheels, where twenty-four Balls were re- 
quirM to draw the Load out of a Hole, inftead of three when the 
Weight was behind and not in a Hole ; it appears that there would 
be required much the fame proportional Force, on Pavement or 
Earth. This Ihews that going into the Country, it is better to 
put Boxes, Portmanteaux, and Footmen behind than before, which 
is the Reverfe of what moft Coachmen do, imagining, according 
to their Notion of great Wheels driving that the Coach will roll 
the better the more it is loaded before. W hereas the Pages wha^ 
are before fatigue the Horfes twice as much as the Footmen that 
are behind. 

COROLLA R T XV. 

B y obferving the Waggon or Cart ftopp'd on the Sand, for 
which a quarter of Force muft be added to each of them when they 
had time to fink, one may conclude that if a Carriage be mir'd, and 
the Horfes are baulk'd in their drawing ; we muft not ftand long,, 
but put on the Horfes behind to draw it out and then go thro" ano- 
ther Place if poflible ; if not, the Horfes muft from fome little 
Diftance be driven briskly, that the Wheels- may not have time to 
fink, and the Horfes may have acquirM fome Swiftnefs, as when 
we go to jump over a Ditch. In making the Experiments, we 
muft not give the Wheels time to fink on the Sand or Earth, but 
lift them up every time when we put Balls into the Bag if there are 

not 



222 A Courje of Experimental Pbilojbphy. 

Left. IV. not enow. One may obferve that even upon Pavement we niuft 
U^V"VJ u fe more Weight when the Load has flood fome time, the adhefion 
of Parts (or rather taking like the Teeth of Wheels) becoming 
greater both on the Axel-tree and on the Pavement, as has been 
obferv'd in the Confideration of Fri&ion. 

COR 0 L L A KY XVI. 

It is alio well when we travel upon Sand, either in dry or in 
wet Weather, to go in the Ruts ? whereby we may avoid the Fric- 
tion on the Sides of the Fellies or Curves of the Wheels, and have 
no Earth to turn up, and alfo the Ground is firmer there. It ap- 
pear'd by the Experiment, that when the Waggon or Cart had 
gone twice thro* the fame Ruts, if it was then drawn in the fame 
Rut the third time, it requir'd fcarce half the Force this laft time 
whether upon Sand or upon Clay, becaufe the Wheels then did not 
fink above half a Line : Therefore in making Experiments to be 
compar'd together, we always fill'd up the Ruts of the Sand and 
of the Clay, that the Difficulty might be the fame in the Cafes 
compar'd. For without that, when the Cart went after the Wag- 
gon, it always had the Advantage in the Experiments on Sand: 
And the Waggon would ftill have loft more if it had gone before 
the Cart upon the Clay. 

C 0 R 0 L LART XVII. 

S e v E i a l other things might alfo be obferv'd concerning little 
Wheels, as to Holes, Heights to be overcome, and other Cafes, 
wherein there will always be found a great Difadvantage : If it 
be not fo great in the Heights to be overcome, becaufe there ap- 
pears to be only the Lots of a third Part; as the little Wheels then 
do not fink deeper than the great ones; yet in other Cafes more 
-than half the Force is loft: So that which way foever we confider 
that Matter, there will always be more Difadvantage than Con- 
veniency. 



0 R 0 L LA R T XVIII 



A s to the Carts with two Wheels, we fee fuffieiently what Dif- 
adyantage they have when compar'd with Waggons of four equal 
Wheels; and if they have any apparent Conveniencies, as that of 



A Courfe of Experimental Phihfophy, 2 2 

load'ng and unloading more eafily, much more is loft than gain'd Led. 
by faving that Labour, which ought not to be confider'd, anymore 
than the greater Eafe of going into a Chaize with low Weeels; 
for we fuffer for it in another Cafe by the rough Jolts, and the 
greater Labour of the Horfe that draws. 

C O R 0 L LART XIX. 

This Reafon of loading more eafily might at rnoft obtain in 
Cities, where we ufe fmall Carriages and often load and unload 
but for Carriages that hold their Load a Week or two without un- 
loading, the greater Eafe of loading fhould be confidered. At that 
rate we might alledge that we fhould only ufe Sledges, rather than 
load upon a Waggon with four high Wheels : But what would be 
the Difference of the Profit ? 

COR O L LA RT XX. 

Do not thofe Carters who ufe Carts to carry Wines with 
very low Wheels, that they may load with the more Eafe, and 
then alfo ride upon the Horfe, deferve to be made to draw the Cart 
themfelves inftead of killing Horfes by needlefs Labour that might 
do great Service if worked moderately ? That Lazinefs is fo much 
the more to blame, becaufe a Turn or two more of the Handle of 
the Jack, or of the Windlafs, would raife up a Veffel of Wine into 
a high Carriage, with fpending very little more time, and fcarce 
taking any more Pains. 

C 0 RO L LA R T XXL 

If the Cart has fome Advantages on account of the Dire£tion 
of the Fore- Horfes, and the Height of the Wheels, it has a great 
Difadvantage for the Tiller, efpeeially upon Pavement ; one Wheel 
coming down from a high Pavement drives one Shaft againft the 
Horle's Flanks, then the other Wheel falling drives the other Shaft a- 
gainfttheHorfe's other Side,fo that the poor Horfe being bangM about, 
efpeeially in great Jolts, is foon worn out or kilPd : So that there 
muft be a great force to draw the Cart upon- the Pavement on 
this account; and even when it is drawn by a String over. a Pulley 
it goes in zigzag. 

C O R 0 L- 



224 A Courje of Experimental Vhilofophy. 

Left. IV •■ 

COR O L L A R T XXII. 

Besides this Difadvantage, the Tiller carries part of the Weight* 
as he goes up the Weight falls back and pulls him, and in going down 
Hill the Weight comes upon his Back; befides he is forc'd to 
flop alone an immenfe Weight that is laid upon the Cart; fo that 
it is a Wonder no more Tiller Horfes are kill'd, tho' People gene- 
rally make Tillers of the ftrongeft Horfes they can get. A Horfe 
thus harrafs'd every way cannot employ fo much Force to draw as 
if he was before, or between the Shafts of a Waggon, where he is 
not bang'd upon the Sides, and has nothing to carry. 

C O R O L LART XXIII. 

W hen we confider how much of the Tiller's Force is loft, 
how much deeper the Wheels fink in than in the Waggon, how 
much more Force is requir'd upon Sand, Clay and Pavements ; we 
may judge, that there is a double Advantage, or nearly, to make ufe 
of a Waggon with four equal Wheels and as high asthofeof Carts; 
for the Dire&ion for the Horfes would then be the fame; and the 
Experiment fhews us how much more Force is requir'd for a Cart 
upon Sand and Clay, where it goes ftreight like a Waggon. 

CO RO LLAR T XXIV. 

Some Carters, when they have new Wheels in their Carts falflv 
attribute to the Prison of the Naves the tiring of their 
Hones, which are twice as much fatigu'd without appearing to do 
any more Work ; for when the Wheels have had a few Turns they 
go free upon the Axel- trees ; and when they are well greas'd they 
go as eafy the fecond Day as any time afterwards ; befides we have 
ihewn that the Friction on the Axel-tree is very little. But the Caufe 
of tins Labour to the Horfes is the quantity of Nails in the Iron Plates 
round the Wheels, and the great Height of their Heads, which is 
about an Inch. This Difficulty of rolling along when there is a 
Space between the Nails, is in the Experiment reprefented by an 
height of one Line to overcome, reducing the Feet of the Wheels 
to Inches, &c. And fince it appears that there muft be twenty 
times more Force, or thereabouts, to overcome this Height of one 
Inch; tho' the Nails fhould be but half an Inch high, one may 

guef s 



A Courfe of Experimental Phikfophy. 225 

guefs how much Labour muft be employed to raife the Weight foLeQ:. IV. 
at every Nail when the fhooing of the Wheels bears upon the Pave-s^v^\j 
ment, and then the Wheel is rais'd up upon the Head of a Nail all 
the while the Wheel goes round, and efpecially where there are 
narrow Gutters. This is the true Caufe of the extraordinary La- 
bour of the Horfes* 

COR O L LA R T XXV* 

This fhews that it is neeeflary the Wheels fhould be round, and 
the Carters who think they fave Money in ufing many great Nails 
(becaufe the Iran Plates or Shooing does not wear fo faft when there 
are fuch Nails) are in an Error, and lofe double by doing lefs Work 
and fatiguing their Horfes. 

COR O L L A R T XXVL 

These Nails alfo have the fame Effe£fc as narrow Plates, they Aide 
between the Pavement and from thence they have a greater Height to 
rife in lifting the Weight up, and fometimes Aiding down again, and 
that wears the Plates round, which makes them Aide more between 
the Pavements and into the Ruts which the Kennels make in the 
middle of the Streets ; and it is alfo upon this account that narrow 
Plates foon grow round, and being round tire the Horfes almoft as 
much as if there were Nails* 

\J Jx \J Ju JLj Ja jtv JL Jxix Y 11» 

T H 1 s {hews plainly enough, that it is advantageous to have the 
Plates upon the Fellies of the Wheels wide, as well on the Pave- 
ment as on the Ground, as it appeared by the Experiment of the 
great narrow Wheel upon the Pavement, and alfo considering the 
Strength that the Horfes i muft exert to draw out the Wheels from the 
'Kmmhy the Damage that is done to the Pavement, and the quick 
wearing of narrow Plates^ which alfo foonbe come round and inconve- 
nient It wotfd be better to have the Kennels like Troughs, wide and 
fhallow, * as IE Fig. 14. and not likeLM Fig. 15, which is the*piate 17. 
common Make of the Kennels in the Streets* Fi g h & *s* 



G 



CO RO L- 



C 0 R O L LA R r XXYIII. 



I f Kennels were made in this Shape feveral Advantages -wou?<3J 
be gain'd: The Plates or Shooings of Wheels would not fo foon 
grow round, nor break the Paving fo eafily : The Pavement of the 
Kennel itfelf wou'd lalt longer becaufe it wou'd not receive fuch • 
great Shocks, every part fupporting more equally whereas now 
the loweil Place bears much a greater part of the Weight, whereby 
it finks moft and fooner breaks. This finking in makes thole Places 
lower when they are mended, , and the Rain-water ftays in therrp 
fo that the Wheels or the .Hones Feet ftriking into them, fplalli the 
People that walk along, whereas the Water wou'd always run 
down into the middle of the Kennel, were it not for thefe Incon- - 
veniencies : ^ neither wou'd the Stream of the Kennel-water grow 
fo wide as it does in great Showers,, becaufe in the Form we pro- 
pofe, the . Kennel is wide enough at bottom to carry offcthe-Wa*- 
ter j and it would be eafier in walking to ilep over them; . 

C O R O L LA R T XXIX. 

T h u s alfo might the little Channels, that bring the Water 
from the Houfes to the Kennels in the middle of the Street, be - 
made lefs: Nay it wou'd be better to be without them, only ma- 
ting a gentle Declivity from the Hbules to the middle of the Street - 
Thefe little crofs Kennels are very inconvenient for thole that walk the 
Streets, nay for the very Horfes and thofe that go in Coaches : Peo- 
ple don't confider that one muft ftop a little at every one of thefe . 
Channels and go irregularly, taking, firft a little Step and , : then a 
great one to ftride over ; and a Htde Stop of the Center of Gravi ty 
or of a Body in Motion tires one . very much : This is- the Reafoij 
why Peopjfe are ^momtir'd^ 

ibvep] in 4tKe, Country, eym p|oii-;P^yempnt, = becaufe, tihei^the Body . 
al^pysj ) continues its. J Motioii ' vyithout Interruption - The fame 
might: happen in Tar is if there was only one Kennel pretty wide 
and {hallow ki the middle of the Streets ; then alfo Perfons that go = 
in Coaches wou'd be. lefs jolted. 



0 R 0 L 



■A €owfe of Experimental PhMo^fiyl 227 

€ 0 R 0 L LA R T XXX/ 

The Ufe of Waggons with regard £0 pavM Streets and to pub- 
lick Roads would alio be- of publkk Advantage^ infiead of Carts, 
which are very .^^g^ to' their Bignefs, and which are 

generallyloaded {0 as Jaendanger the breaking of all the Geer. 
The valV^ieighr fupported on two Points^ 

as they have 1:^ finM deep and makes great Ruts in' 

the Ground ; and upon 3|a^ the Wheel is bora up on a 

Nail Head and comes to fall down again, it prefles down or breaks 
that Pavement worfe than if ten or twenty Waggons with as hea- 
vy a Load had pafs'd over that Place. For a Waggon Wheel, that 
falls upon the fame Place and from the fame Height, comes down 
but with half the Weight that the Cart W heel does, and therefore 
ftrikes it but with half the Force. Now the Pavement being fome- 
thing of the Nature of Glafs, will not break unlefs it receives a 
fufficient Blow, and an hundred Blows, if each of them be lefs 
than that fufficient Blow, will not break it. The Blow from the 
Cart in thofe Places is often fufficient to break the Pavement where 
an hundred Blows from a Waggon Wheel, as they ftrike but with 
half the Force, will not be able to hurt it : So likewife will a Wag- 
gon pafs over as often as you will where a Cart would fink in. Carts 
therefore, little Wheels, narrow Plates for fhooing the Fellies^ and 
great Naikj are to be avoided as much as can be. 

CO R O L LA R T XXXL 

B y the Experiment made upon Clay and upon Sand, we may 
fee how ufeful it is to have the Roads firm and folid, fince there is 
fo much Difference between the one and the other. And certainly 
the Carriage of Goods, by Land or Water, contributes much to the 
artificial Riches of a Kingdom or State : And all things well conii- 
der'd, we fhall find that the Time and Expence employ M ''in mend- 
ing Roads, is the moft for the publick Advantage, 

C O R 0 L L A R IT XXXII© 

In this and the other three following Corollaries Mr. C a mu s 
■finds fault that the Laws and Orders concerning mending Roads 
snd Matters relating to Carriages are no better obferv*d f and 

<3j* 2 -takes 



228 ACourfe cf Experimental Philojbphy. 

Left. IV. takes notice that a Farmer that u/es many Horfes to draw a 
t/YXJ large Cart very heavy loaded f may /foil theRoads for many Miles \ 
worfe than an hundred others with the common Carriages,, and 
therefore fropofes in 

COROLLAR T XXXVI. 

That Orders ftiould be made for the publick Good, That on- 
ly two Horfes fliould draw in a Cart and four in a Waggon, which 
Four would do more Work than fix in a Cart, 

COROLLA RT XXXVII. 

That Wheels of Carriages, never be made lefs than four Foot 
and a half, or five Foot in Diameter ; that the Plates of Iron never 
be lefs than three Inches wide, the Fellies three Inches and a quarter 
deep, atleaft for Coaches, and four Inches for Waggons or Carts, 
which by that means would be ftronger as they are broader. 

CO RO L LA RT XXXVIIL 

That the Nails for the Plates be made without Heads, and that 
a great many be made long enough to 20 quite thro' to be vl- 
vetted, which will keep the Irons from rifing up. For two Nails 
fcrew'd behind, or with a Counter-Rivet will hold the Irons on 
falter than fix with Heads. One may as. well make the Plates three 
Inches wide as two, and as they wear out more at the Edge, they 
may be made thinner in the Middle next the Fellies, in the Shape 
#pi.i 7 .F.i6. fhewn in the Seftion, Fig. 16. at B C, * which may be eafily 
done in the forging by help of a Swage of that Shape. Thefe 
Plates being put on hot will preferve the Fellies more from crackings 
laft as long as others, and neither be heavier or coft more. By this" 
means, the Roads would not be fo foon fpoil'd, and all that ufe Cai~ 
fiages would find their Advantage* 



COR O L LA R T X: 

The Naves of Coach Wheels ffiould be made a little thicker ib 
the middle, and not be bor'd quite thro' where the Spokes are let in y 
for then their Ends wou'd not. receive the Greafe, and thereby be fo apt 
to get lpofe : The Naves might alfo be made fifteen, or fixteea Inches 



A Courfe of Experimental Pbihfophy. 2 29 



long, with the great End a little lefs, fince the greater Length of e the Left. IV* 
Nave does not encreafe the Fri&ion, and it holds the Wheel ftreigh* w^v"n^ 
ten The Spokes Aiould alfo be made an oblong Square at Bottom^ 
to have a Shoulder to keep them firmer than when they are rounds 
as they are ufually made. The Spokes thus fix*d would not be lb- 
apt to fly out nor make that ratling which they do, efpecially in 
Summer-time. The Workmen may work out thele Shoulders with 
a Bevil at the fame Angle that the Spokes are let in, to make the 
Wheels difhing out, after the manner the Joiners make their Skew 
Tenons, and the fame Inftrument would dire£i them in cutting the 
Mortaife, ® c. 

Mr. Camus ends his Confederations itp$n this SubjeB with 
obferving that a Toft Chaize with two Wheels has all the Inconve- 
niencies ob fervid in Carts f and befedes has the Ineonveniency of the 
fecond Horfe which draws on one 9 Side ; therefor e % for the Eafe 
of the Horfe s as well as theTravellers f he would have all thofe 
Chaizes to have four Wheels ^ and the Driver pot to ride f but 
fit on a Box like a Coachman^ and the Fore** Wheels as high as the 
hind ones. 

B e sides the Fri£Hon already explained, there is another Impe- 
diment to Motion in feveral Engines, and that is the Difficulty with 
which Ropes are folded, which encreafes according to the Bignefs 
and Stiffnels of the Rope, the Weight which they bear, and the 
Smallnefs of the Diameters of the Bodies about which they wind. 
This Impediment we fhall alfo call Fri&ion, becaufe we mult make 
Allowance for it as well as for the rubbing of the Parts of the 
Machine, otherwife we fhall always find the Effe£k of Powers by 
means of Engines to be lefs than we expe£b 

Monfieur *Perauh y in his Comment upon VitrttvmSi defcriBes 

an Engine of his contriving, whereby he thinks to avoid all Eri£fci~ 

on. This Machine is an Axis in Teritrochio applied 1 a new Way^ 

But as he is not aware of the Fri£lion or Hindrance that arifes from; 

the Difficulty of bending the Ropes, the Effe£fc will by no means* 

anfwer as lie proppfes; for upon Tryal, his Machine appears to" 

have more than double (fome times than triple, or quadruple) the 

Fri&ion of the fame Engine us'd in the common Way*, when the 

Pivot or Iron Axis is in Diameter the iQth Part of the; Roller or 

wooden AxeL He- does indeed fay that the Machine was tryM and 

focceeded ::, 




iLea. IV ; fucceeded j. but: .having carefully examin'd it, I found it impofllble 
uTsTXJ to anlwer according to the Delcription ; .and left at any time any 
body fhould :be at the fruitleis Expence to make the Machine in 
large, I demonstrated the |>ifadvantage of it before the Royal Soci- 
ety, and fliewUthat beiges the Fri£rion (overlooks by its- Author) 
there was a,, great inconvenience in the Application • And this I 
confirm'd , by Experiments made on a Model of an Inch to a Foot, 
ithe large Pulley or Wheel being fuppos'd of Five Foot. ; 



Monfieur Veraukh Account of his: Engine is as follows : « In 
M Imitation of the ( modern ) Crane, I have invented two Engines 
M for railing Weight. The firfl: is made of that Organ which is 
« the moft advantageous of any in Mechanicks for facilitating Mo- 
" tion; becaufe it is free from that Inconveniency which we meet 
■ u with in all others; namely, the Fri&ion of tfie Parts of Che Ma- 
"** chine, which renders their Motion more difficult. This Oman is 
« the Roller, which Ariftotle prefers to all other Organs, becaufe 
* all the others, as Wheels, Capftanes, and Pulleys, muft neceffarily 
■ di rub in fome of their Parts. But the Difficulty was to apply the 
" Roller to an Engine that raifes Weights, its Ufe having only been 
" hitherto to caufe them to roll on an horizontal Plane. The Engine 
* Plate 17. « which Ipropofe has a Bafe AAB,* JJPlate 17, Fig, i 7 .) fome- 
!6- r 7' -« thing like the Crane ; This Bafe has in its upper part the horizon- 
•* f al p i ece B, which clafps an upright Shaft C O, fupported under 
" its Pivot O, on which the whole Engine moves in the lame man- 
neivas the Crane, when the Weight is to be lower'd. This Shaft 
" fupports on its Top a crofs Piece D D, to which are faften'd the 
" Ropes E E, which wrap round the Barrel, Axel, or Roller F, 
" which has another Rope G, that alfo wraps or winds round one 
" of its Ends. This laft Rope is that which raifes the Weight. At 
" the other End of die Axel there is a great wooden Wheel like a 
" Pulley HH, about which is wound a long Rope N. To work 
" this Engine, one muft pull the long Hope N, which caufing the 
' great Wheel to turn, does alfo carry round the Axel or Barrel* 
" which is made faft to it. This Axel, as it turns round, caufes the 
M Ropes EE to wind about it, and therefore the Axel and the Wheel 

Z ? fe ' . whilft the Ro P e F > to which the Weight is faften'd, does al- 
fo wind itfelf upon the Axel the contrary way .; and this double 
"winding up of the Ropes makes both the Burthen and the Axel 
'! ^d Wheei to rife at the ikme Time. Now it is evident, that all 
this Rife is perform'd without the Friaioa of aiiy Part, and confe- 

quently ? 





* quently, die whole I*bwer which draws the Rope N, is %mpIoyMLea:v 1^ 
4% without any Hindrance >,, which cannot be in otfe En^ineSa^ 

a It may Be oBJe£$ed that the Power which a£fe at mult, be- 
fides the Weight* raife alfo the Axel and great Wheels and that 

* their Weight is one of thofe Obftacles which Ariftotle lays all En- 
gines - are liable to ; : and that this Obftacle is equivalent to the^ 

# Fri&ion which is in other Organs. But it may be anfwer'd, that 
« Fri&ion is an Obftacle wholly unavoidable in all other Organs; 

but that it is eafy to remedy the Obftacles of this/ which - is done 
by means of the lieavy Body< M r taken equal in Weight to the 
^ great Wheel and Axel, which it luftains by means of theRbpe 11^ 
^ which running over the Pulleys L L 5 is fix'd to the Ring or Collar 
iC K that goes round the Axel R For the Axel and the Wheel be- 
a ing counterpoised by this Weight, the Power which a£fcs by draw- 
^ ing the long Rope N, a£ts for raifing the Weight only. The Ex- 
^ periment which was made with this Engine has confirmed the 
^ Truth of this Problem, by comparing its ? Eftfe&s with thole of 
& a Crane,- in which the Proportion of the Bignefs of the Axel to 
^ the Circumference of the Wheel, was the fame as in my Machine. 
tt For it hap£en ? d that in the Crane, a Weight of One hanging at 
Rope going about the Wheel, drew- up a Weight of 1 Seven^ ^ 
^ when it ikd one Half added to make ir preponderate, or give 
Motion to the Power : And when the Weight to be raisM, and" 
^ the Weight which ferv'd as a Power, were proportionably en- 
a creas'd, there was alio a Neeeffity to encreafe the additional 
^Weight, which made the Power preponderate in the lame Propor* 

# tion : So that Ss4t was required to add one half to the Powerwhen- 
^the Weight wte^lVt^^^he- Addition t&- the Power became^O^ r 
** : forW Fourteen ; Pbund Weight,-^-^^. for a Twenty-eight Toi&d^ 
^ Four for ^Fifty-fix Pound, and fo on ; becaufe- the /Refinance fropa- 
^iPrifibion enereafes nearly in' the-: fame Proportion" that : the -Weights - 

a! are encreasM* 'But this;"did-not- happeh in' my^Enginef^in which- 

a 'om ^Mrfer --was alwas fuiKdient fer the Draught' • ( or to ; make : 'thfe-.'.- 
a "P6wer preponderate } not only when the Weight was Seven, tbuCr 
a alfo when it was Fourteen Pounds, twenty-eight Pounds, Fifty-fix^ 
^ Pounds, &c. which evidently fhews^ that t^is Engine a£ts with*. 
a out Friction*'* 





T h us far - Mbnf^ermltv But 
ion may appear, a little Attention will En< 

sine 



s 3 2 ^ Ctf«r/fc of Experimental PMIo fa 



Le£h IV. gine had no Fri£Hon, yet it Is more inconvenient than an Jxix in 
s^^sr^j 'Peritrcchioj with the fame Proportions; and likewife that it has 
■* pi. 1 8. f. i. more Fri&ion than the fame Machine in the common Ufc. ACE ^ 
( Fig, t • ) is a common Axis mTeritrochio^ which has the Wheel 
AE, five times] bigger in Diameter than the Axel; fo that A C 
the Radius of the Wheel (which is the Diftance of the Pow- 
er) is to CB the Radius of the Axel ( the Diftance of the Weight) 
as 5 to i : Confequently One (for Example one Ounce, as in our 
Experiment ) will keep Five in /Equilibria. Now tho 5 the Fricti- 
on of the Gudgeon at C is unavoidable, yet it may be diminifh'd 
t Ann. 4. by diminifhing the Diameter of the Gudgeon f. Provided it re- 
mains ftrong enough to fuftain the Machine and its Burthen. Here 
one Penny Weight, or % \ of the Power added to it, makes it pre- 
ponderate, and give the Machine Motion with a due Velocity. 

Now this very Engine made Ufe of in Monfi. TeraulfsWzy^ 
does 1 fo alter the Diftances of the Weight and Power, that inftead 
of One for our Power, we muft have Two and a half to keep the 
very fame Weight Five in Mquilihrio^ as may appear by a Sight 
*.*Pi.i8.F.2.of the fecond Figure, where fince in the Adtion of the Machine, 
when we pull the Rope PA, we make the Axel DB to wind itfelf 
up upon the Rope H D, it is evident that D is now become the Center 
of Motion, D B (the whole Thicknefs of the Axel) the Diftance of 
the Weight = 2 ; and the Diftance of the Power is reduced to A D 
— 4* So that if two Men, having been employed in the common 
Way to raife Weights equal to the Strength of ten Men, an Engineer 
fhould alter the manner of working, and fit up the Axis inTeritro* 
chio in Monf. Teraulfs Way, inftead of gaining an Advantage, 
Ann. 5. he muft call in three more Men to perform this Work. *\\ If 
it be anfwer'd, that what is loft in Strength will be gained in Time, 
it may not only be laid., that one cannot always call in more 
Help on a fudden, but that even then, tho' we fhould not call this 
an Inconveniency, yet there will be ftill more Fri£t:ion in this than 
in the common Method ; for the Roller or Axel will find a Diffi- 
culty to wind on the Ropes, becaufe they are not perfe&ly 
pliable, and the lefs fo, the greater the Weight is that ftretches 
them. This, together with the Friffcion of the Collar of the Rope 
of the Counterpoife t0 the Engine, makes the Hindrance greater 
than in the common Way* For it appears by my Experiments, 
that when the Power is become equal to 2 f to keep the Weight 5 in 
ALquilibrio+therQ muft be added j (here four-penny Weight) to put 
the Power in Motion, And 



A Courje of Experimental Philofophy. 2 35 

A^d, to fh^w that this Fri&ion of the Ropes is not always the Le£h I V« 
fame as Mopf. "Per auk fuppofes it ; when P (or the Power) is^^v^^ 
made otAy one Ounce, and W ( or the "Weight) 2 Ounces, then Pi ' 189 F# *° 
to make the Power preponderate, only 2 Penny- weight and 18 
Grains was fufficient. But When P is = 2 |, and W =' 5, the 
additional Weight mark'd f was 4 Penny-weight and 2 Grains. 

It is plain from this, that Monf. Teraulfs Experiments were 
very inaccurately made, and therefore not to be depended upon* 

/ have been the more particular here ; becaufe we are apt to be 
led into an Error by the Over -fights of a Man of great Refuta- 
tion^ whom we don*t eafily fhfpeil of a Miftake. 

Tho* it be as difficult, at leaft, to give a certain account of the 
Forces required to bend Ropes of different Diameters, (ftretch'd by 
different Weights, in making them go round Bodies of different Big- 
neffes) as to give an exa£t Theory of Fri£tion : Yet to confider nothing 
of theLofsof Motion occafionM thereby, would be as prejudicial to 
the Practice of Mechanicks, as it would be to overlook the Fri£iion of 
the Parts in En gines. Therefore, tho' the different Materials of which 
Ropes are made, their different Stiffhefs, according as they are more 
or lefs twifted, and fometimes the Temperature of the Weather (as 
to Moifture and Drynefs) at the Time that they are usM, makes it 
very difficult to be exa£t in our Conclufions ; yet we think it is of 
great Ufe to give the beft Theory we can, and mention fome of 
the Experiments, at a Medium, made upon Ropes pretty good in 
their kind and moderately twifted ; becaufe if any part of a Rope 
of any Length of equal Thicknefs and even Twift from End to 
End, be ftretch'd by a known Weight round a Cylinder, Roller, or 
Pulley, and it be obferv'd what Force will bend it about a Roller 
of a given Diameter, we may know, what other Force will b% re- 
[uir'd to bend it round any other Body, and when ftretch'd with a 
ifferent Weight : and befides, in new well made Ropes, the Diffi- 
culty, of bending, cater is paribus^ is pretty near as the Diameters 
(not the Solidities} of the Ropes. 

Experiments, Tlate iP. Fig. 3. 

To two immoveable Hooks RR I fixM the two Ropes Rr, Rr, 
at the Diftance of about 8 Inches from each other ; and at the lower 

Hh End 



2 34 ^ Courfe of Experimental Thtlqpiphy. 

Left. IV.Endof the Rope I hung the Scale S3, on which I placed the Weights 
l/vv W to ftretch the Ropes . Then I tool? fucceffi vely three Cylinders 
pi. 18. F. 3 • iii^ e CQ each one Foot long/ (one of half an Inch, another of an 
Inch, and the third of an Inch and an half Diameter) and having 
wrappM the two Ropes about one of the CyliiKJeirs 9 as may be feen 
in the Figure, by putting Weights in the little Scab s by means of 
the Ribbon m I brought down the Cylinder* towards W, always 
taking care that the Parts of the Ropes did not rub againft each o- 
ther, and rolling the Cylinder up and down two or three times be- 
fore I fettled the Weight that I obferv'd to bring down. 

N. B. The Weight includes the W eight of the Cylinder and 
Scale* 

IPL18.F.4. In the 4t h Figure f C repreients the SeftiQiiof the Cylinder or 
Roller about which the Rope Rr is wound, and K L its Diameter^ 
and m s the little §cale and Ribboa as before. 

The Weight W may be always look'd upon as the Weight 
ftretching the Rope; becaufe (tho' it ftretches the two Ropes, 
* pi s f confequently each Rope is ftretch'd but by half of it) the Cy~ 
: pl is. - 3 * linder CC * brought down by the Weight s bends or eaufgs a 
folding in the two Ropes at C and C 9 which gives it the fame Dif- 
ficulty of Defcent, as if only one Rope bearing the whole Weight, 
was folded about it. 



A T Jk B L 



A Courfe of Experimental PUhfophy. 



23? 



A TABLE of Experiments., fhewing what Fortes Le 
were requir'd to bend Ropes of different Diameters, 
flretch'd by different Weights, round Rollers of diffe- 
rent Bignefles. 



The Quantity of the 
Weight W, by 
'which the Rope is 
ftr etctidy exprefs*d 
in^fa Averdupoids. 

60 Ifc— • 


TheReJtftance of the 
Rope about a Cylin- 
der of half an Inch 
Diameter, exfrefid 
in § Averdupoids. 

C 2 25 if 
\ 96 — 

6 45 


tfheRefiftance of the 
Rope about a Cylin- 
der or Roller of one 
Inch Diameter in 
5 Averdupoids. 

113 f ? 

4$" — 

2 2 # i - 


Reffiance a- 
bout a Roller of one 
Inch and half Dia- 
meter in ^ Averdu- 
poids. 

75 5 
go — 
15 — 


Diameters of the 
Ropes of 3 Strands 
or Ihvtfls, exprefs^d 
in tenth Parts of 
an Inch* 

— 0,5 

— 0,2 

— 0,1 




C 150 




75 — 




5° — 


— c,5 


4 0 lb — 


I 60 




30 — 




20 — - 


— 0 ? 2 




I 30 




1 5 — — 




10 — 


— c,t 


20 ib— 


r 75 — 
< 30 — — 

t 15 — 


37 \ — 
15 — 

7i — 




25 — 
10 


— 0,5 

— 0,2 
— C,T 



* The Experiment could not be made her ej becdufe the Cylinder 
of if Inch diameter j which Jbould have been us d here ^ weigh* d 
above % Ounces i and the Weight requir'd to bend the Rope r ap- 
pears by Analogy to be but 5 Ounces. 

Observations on the foregoing Table. 

The Experiments mentioned here are taken at a Medium from 
a great many that I made, the Difficulty of bending the Ropes 
being fometimes a little lefs, and fometimes a little greater. 

One may from this Table make a more extenfive one, by put- 
ting in Numbers analogically for feveral other Thickneffes of Ropes 
and larger Diameters of Cylinders or Rollers ; but in Ropes of a 
Diameter bigger than hair an Inch, a Roller of half an Inch is 
too little and hardly ever us'd in Pra&ice; nay, in fuch Cafes the 
bending of the Ropes is more difficult than in Proportion to the other 
Experiments; and in my Tryals, the Rope of 0,5 of an Inch Dia- 
meter generally requir'd more than here fet down. 

H h 2 I found 



2^6 A Courfe of Experimental PMIofophy. 



Left. IV. I found that a woven Clock-line of 0,1 Inch Diameter required 
(/W more Force to bend it than a twifted Rope of the fame Thicknefs 
which feemM much ftiffer ; but if we confider that the woven String 
flattens as it folds round a Cylinder ; that has the fameEffed as if the 
Cylinder was become lefs, one Fold of fuch a Line making by its 
central Parts a lefs Circle than a twifted Rope, which does not be- 
come flat. 

MoKs r . Amontons made feverd Experiments of this kind, menti- 
oned in the Memoirs of the Royal Academy of Sciences at Paris, 
for the Year 1699, and calculated a Table of the Force required to 
bend Ropes, which Table I cannot recommend, becaufe it is built 
upon a Miftake ; for he fays, that the Difficulty of bending a Rope of 
the fame Thicknefs, and loaded with the fame Weight, decreafes 
when the Diameter of the Roller encreafes, but not fo much as that 
Diameter encreafes ; but I have found by many repeated Experiments, 
that the Difficulty decreafes direfHy as the Diameter of the Roller 
encreafes. That is, TheT>iffictilty of bending a Rope round a Roller f 
is, caeteris paribus, inverfly as the^Diameter of the Roller, N.B« 
I believe Monf Amonton\ Miftakearofe from the Parts of the Rope 
rubbing againft each other, which I always took care to avoid. 

When a Rope is carried under or over the Wheel or Slieeve of a 
Pulley, the Difficulty of bending is as great as if it went quite 
round a Roller, which will appear by obferving the ^th Fig. of 
"Plate 18; For while the Rope is folding about the Cylinder G in 
theDire&ion r K L, the under Part L 0 K unfolds of itfelf without 
any Difficulty. 

I have in this Le£ture (Page 187, 188, 189) given Rules for 
the Fri&ion in a compound Engine, arid IbewM the Application of 
fhofe Rules by an Example ; but did not then take in the Difficul- 
ty of the folding of Ropes. But now I will give another Example 
wherein that alfo is confider'd, and fhew how near the Theory a- 
greed with the Experiment performed with a Machine made as nice- 
ly as poffible, to make the Companion the Jufter. 

The Machine confifts of three Pulleys (two upper and one 
tower, or a Tackle of three) whofe Diameters are exa&ly as fol- 
lows, viz. two Inches, one Inch and a quarter, one Inch and an half; 

and 



A Courjh x of:-E>^nnimial Thilofophy* 237 



and all the Center-Pins of one quarter of an Inch Diameter exa£tly,Le£t. I¥« 
and the Rope of one tenth of an Inch Diameter. The Weight is 1 8 w^v^ 
Pound AverdupoidS) and confequently the Power to keep it in 
JEquilibr 'to muft be 6 Pounds, and a very little more muft make 
the Power raife the Weight, if there was no Fri&ion; but here 
no left than 20 Ounces are requir'dy tho r the Machine be very 
exa£t« 

I have {hewn ^lnlJRuk ?. 'Page 187.) that two thirds of thepi x § 9 F. 
Power are equal to the Fri&ion of a Cylinder whofe Surface moves 
as faft as the Power, and whofe Gudgeons are equal in Diameter 
to the Cylinder. Now as the Diameter of the firft .-Pulley 1 . : is< 
eight times bigger than its Pin, its Friftion muft be 4 Pound di- 
vided by 8, or d. Ounces ; becaufe as the Surface of its Circumference 
moves: with the lame Velocity as the Power, its rubbing Surface on 
the Pin muft move eight times flower* 

The fecond Pulley 2jj; whofe Surface moves as flow again as the 
Power, and whole Pin is fix times lels in Diahcieter than itfelf, 
muft of confequence have its Fri&ion orily of 5 ^ Ounces; be- 
caufe two thirds of the Power, or 64 Ounces, muft firft be divided^ 
by 2, by reafon of the Velocity of the- Pulley's Surface being but 
half that of the Power ; and then again by 6, becaufe the Pin be- 
ing fix times lefs, the Parts rubbing on the Pin muft ftill move fix. 
times flower. So that — 32, and ^ ^ 5 f Ounces. 

The third Pulley 3, moving with: a third of the Velocity of the 
Power, 64 Ounces, muft be divided by 3, and that Quotient again^ 
by 5,. becaufe the Pin is here j of the Diameter of the Pulley ; fo 
that the rubbing Parts of this Pulley have their Velocity one 5 th 
of a gd, or. ,7, of the Velocity of the Power ; and therefore \% 
will give 4,^6 &c Ounces. Now the Sum of all thefe Frictions 
(viz. 8 Ounces 4- $,3333 &c Ounces, 4,16 &c. Ounces) makes, 
j 7,6 Ounces, which is the 5 th & £ part of the Power. This Addi- 
tion to the Power will fo encreafe the Fri£tion, as to require a 
Super-addition of the $ >th&- x * part of that firft Addition, and fo 011, 
in this Series, Ounces -f~ 3,2 Ounces (which is 77^) -+-0,59 

Ounces (which is j~) &c. in all 21,4.1 Ounces., 

To his muft be added the Fri&ion or Refiftance on account of* 
the Difficulty of bending the Ropes, which by the laft Table may 
be found in the following manner* Suppose 



2 g8 A Courfe of Experimental FhUofophy. 



Le£t IV. Suppose the Part of the. Rope, which is at i the Side of the firft 
^r^J or upper Pulley to be fixM, then will the 3 Ropes DE, 3 B, and 

*PU8.F. 5. 2 A fuftain together the whole Weight W, * which (together with 
the Block) weighs 18 Pounds, fo that we may confider each Rope 
as ftretch'd by fix Pounds, and folding round different Cylinders of 
the refpe&ive Diameters of the Pulleys. 

For the firft Pulley, we look in the. Table for a Rope of one 
tenth of an Inch,- and find that when Hreteh'd with the Weight of 
20 Pounds it requires 7,5 Ounces to bend it round a Roller of an 
Inch, therefore we muft firft make Ule of this Analogy* 

As 20 ft> ftretching a Rope of bne tenth of an Inch in Diameter i 
Is to 7 I Ounces, the Force requir'd to fold iti on a Roller of 
one Inch Diameter : : 
So is 6 Pounds, when fo much only ftretches the Rope : 

To 3,25 Ounces .(that is, two Ounces and a quarter) the Force 
able to fold the lame Rope, only ftretch'd with 6 flb, round a 
Cylinder of one Inch Diameter. 

But as the firft Pulley is not of one but two Inches Diameter, 
we muft diminifh the Force neceffary to fold the Rope in a re- 
ciprocal Proportion of thofe Diameters, by the next Analogy, 
which will alfo ferve for the two other Pulleys* 

As the Diameter of the Pulley, where we want to know the 
folding Force : 

To the Diameter of the Pulley where the Force is known : : 
So is the folding Force before found : 
To the folding Force required. 

That is, as 2 : -7 :: 2,25 : 1, 1 2 5 Ounces, for the ift Pulley ; 

And, as r,5 : 1 :: 2,25 : 7,5 Ounces for the 2d Pulley ; 

And laftly, as 1,25 : 1 2,25: i,8 Ounces for the 5 d Pulley, 

By fuch Analogies we r inay ^encreafe the little Table above to any 
other "Proportions^ fo as to /hew by Infpeffion the Force required 

to 

* It is true, that in Motion^ Qne Rope bears more of the Weight and another lefs of it ■ 
but upon the whole, the different Difficulties of folding the Ropes taken together , do ill 
mount to the very fame* So that this is the beft, becaufe the eafeji vcay of confider ing it. 



ACourJe of Experimental Phikfophj. 239 

to fold Ropes in moji Cafes \ or mo ft Cafes may be deduced ■ jfrtf«Le&;iv \ 
this Table it f elf L/ m ST\J 

But to go on with the Theory of theFri£Honof our Machine * 
Theft three laft Friftions, or Refiftanees of Ropes added together, 
make 4,425 Ounces, which- added to 21,41 Ounces the Fri£Hon a*- 
bove found, gives in all 2^,835 Ounces, a Friftion greater by near 
fix Ounces than the Experiment gave. But I have demonftrated in 
the Annotation to my third Le&ure (Tag? 1^4) that, When a 
String or Rope rims over a Jingle T alley or Roller by the De- 
fcent of the preponderating Weight {the other Weight rifing at 
the fame time) the Trejfure on the Axis of the Tulky is always 
€({ual to the Quadruple of the "Product of the W tights multiplied 
into one another r ana 1 divided -by 5 the \$um*of. the. fame Weight si 
And that Prefiure being always lels than the Sum of the two 
Weights, when they are unequal, To much as it is lefs muft be 
taken out of the Account of all the Friftions, and the Experiment 
then will be extremely near the Theory. But to omit nothing in 
our Calculation, we will alfo examine what this Diminution of 
Preffure is. 

The Power / 6 Pounds ) together with what we have fpund ne-pi. 18. R 5. 
ceffary to be added to it on account of all the Fri&ions and Refi- 
nances of the Ropes, is to be look'd upon as the preponderating 
Weight in the Cafe of the Propofition abovementioned, that is, 6 
Pounds and near 2 6 Ounces, or i 3 2 Ounces : and 6 Pounds without 
my. Addition is to be confidered as the Weight overpoized on the 
other fide of the firfr Pulley i , which is an upper Pulley. Let the 
two Weights be multiplied together, that is, 6 Pounds or 96 
Ounces x 1 22 Ounces, the Product of which is 11712 Ounces; 
whkh again multiplied by 4, or 1 1712 X 4 gives the Produ£i -46848: ;.. 
then dividing the laft Produ£t by 2 1 8 (the Sum of the Ounces in 
both Weights) or ~4fjp, the Quiotient will be 214,9, which fub~ 
tra£ted from 218 the Sum of the Weights, will give 3,1 Ounces 
the diminished Freiure, m: 4hu part of the Fmffwc which the Pin 
of the Pulley 1 is foeed from when the Power prepond^atirig runs 
down. 

Now as there is another upper Pulley over which the Rope al- 
fo runs, there muft he likewife taken off oa that account 3,1 Ounces 
Sp that if thefetwo lafi: Sum% or 6,2 Ounces be takwirom 2 S ? 8§s 

Ounces 



240 Courje of Expend Philofopfty. 

Left. IV. Ounces found by Theory equal to all the Fri&ions, there will re- 
s^-v-^o main 19*635 Ounces, the Addition neeeffary to make the Power 
over-balance the Weight with the leaft Augmentation poffible ; 
and that in the Experiment is 0,3 65, or a little more than one 
third of an Ounce ; for 20 Ounces added to the Power 6 Pounds 
makes it run down. 

N.B. Nothing was here allowed as an Encreafe of Friffion 
on account of the Weight added to bend the Ropes., which 
would ft ill bring t Be Experiment nearer the Theory* 

In Pra£tice we need not make this laft Allowance, or confider 
this Diminution of PrelTure, efpecially in Tackles of many Sheeves, 
becaufe there are generally fome Hindrances more than the com- 
mon Fri&ion; as for example/ when Sheeves rub againft the Sides 
or Cheeks of the Blocks, or when their Hole wears bigger, which 
encreafes the Friction as much as if the Pin was become fo much 
bigger. 

Being willing to try how far the Theory of Fri&ion and bend- 
ing Ropes would agree with fuch Tackles of Pulleys as are com- 
monly usM in Building, and confequentty be ufeful to dired our 
Practice, I made the two following Experiments. 

Experiment I. 

I took a Tackle of five Brafs Sheeves in Iron Frames or Blocks; 
that is, three Sheeves in the upper Block and two in the lower. 
Having made msEquilibrium by hanging one hundred and a quarter 
at the lower Block, and a quarter of an hundred at the running 
Rope, I added 1 7 Pounds and an half before the Power could go 
down and raife the Weight. 

Experiment II. 

Two hundred and an half being balanced by half an hundred, 
the Addition of 2 8 Pounds made the Power raife the Weight. 

N.B. The Sheeves were 5 Inches diameter the "Pins half 
an Inch^ and the Rope three quarters of an Inch. 

In the firft Experiment 17ft and an half exceeds by 4 f ft, 
the Sum of the Fri&ions and Refiftances deduced from the Theory. 

But 



A Courfe of Experimental P 




But in the fecond Experiment 28 tfe exceeds the Sum of the Fri&i- Led. IV 
ons, &c. not quite 'x fe. The Reafon of this appear'd to be, that 
the Rope at firft was too big for the Cheeks that held the Sheeves; 
but in the fecond Experiment, where the Rope was more ftretch'd, 
its Diameter became fomething diminifli'd, and fo brought off the 
Rope from rubbing fo hard againft the Cheeks. 

From knowing the Quantity of Friftion in fuch large Tackles, 
we may know what to expect in Practice. For if one Man, who 
for a fmall time can exert the Force of 100 If , thinks that he may 
draw up a Stone or a Roll of Sheet Lead, or any other fuch 
■Weight to the top of an Houfe with a Tackle of Five (be- 
caufe this would feem feafable from Mechanical Principles) will 
find himfelf miikken on account of the Friction, which will not 
be furmounted without an additional Force of 50 lb. 

/ hope this Account which I have given of Fr iff ion and Hin- 
drance to Motion in Mechanical Engines (however imperfect it 
is) may be of con fider able Vfe to direct fuch S P erf ons as concern 
themfelves with Engines a%d Manufactures. And to afford all 
the Help I can upon this Subject s I will give him fame Confede- 
rations of the comparative Strength of Men and HorfeSj as well 
as the befl way of applying their Forces^ being the Refult of ma- 
ny Tears Obfervations of my own, as well as what I have found 
in Authors who have treated of thefe Things. 

An Horfe draws with the greater! Advantage, as we have al- 
ready fhewn from Mr. Camus, when the Line of Direction (be- 
ing parallel to the Plane on which the Weight moves) is level with 
the Horfe's Breaft, and is able in fuch a Situation to draw 20 
eight Hours a Day, and walking about two Miles and an half an 
Hour, which is about three Foot and an half in a Second. And if 
the fame Horfe is made to draw 340 ife he can work but fix Hours 
a Day, and cannot go quite fo faft ; and in both Cafes, if he carries 
fome Weight, he will draw better than if he carried none. We 
don't mean by this what an Horie can draw upon a Carriage; be- 
caufe in that Cafe Friction is only to be overcome, fo that a mid- 
dling Horfe well applied to a Cart, will often draw above 1000 1fe ; 
but fo much as an Horfe could draw up out of a Well over a An- 
gle Pulley or Roller (made to have as little Friction as poffible) is 
properly what an Horle can draw ; and Horfes, one with another, 

I i draw 



24.2 ^ Courfe of ExperimmtalPhilofophy^ 



IV. draw about 200 ib In fuch a Cafe as we faid before. To this* 
uTV^V may be referred the working of Horfes in all forts of Mills and 
Water-works,, where We ought to know as near as we can, how 
much we make every Horfe draw, that we may judge of what 
the EfFed will be when proper Allowance fhall have been made, 
for all the Fri&ions and Hindrances, before we caufe any Machine 
or Mill to be erected* 

When an Horfe draws in a Mill, Water- work, or Gin of any 
Kind (in which the Horfe is made life of to draw round a Cap- 
ftane oxAxisinTeriirochid) great Care fhould be taken that the 
Horfe- Walk be large enough in Diameter, other wife the Horfe 
cannot exert all his Force as he goes round ; for in a fmall Circle 
or Horfe- Walk, the Tangent (in which the Horfe fhould draw) 
deviates more from the Circle in which the Horfe is obliged to go ? 
than it does in a great Circle- The Horfe- Walk fhould not be. 
lefs than 40 Foot in Diameter, when ever there is Room for it ; 
and the fame Horfe lofes of his Force confiderably in a fmall Walk^ 
becaufe he pulls in a Chord of the Circle, drawing the horizontal 
Beam behind him at acute Angles, fo much, that in a Walk of 19 
Foot Diameter, I have known an Horfe lofe 1 fifths of the Force that 
he exerted in a 40 Foot Walk. Mofl of the Mill-wrights in Lon- 
don (and I believe in moft great Cities) do not love to make large. 
Horfe- Walks, even when they have Room ; becaufe, as there is ge- 
nerally want of Room where they have been obliged to fet up 
Works, they have accuftom'd themlelves to make their Geers for 
fmall Horfe- Walks, and think it enough to give the fame propor^ 
tional Velocity to the Power and Weight as is done in a larger 
Horfe-walk (becaufe if the Cog-wheel be fo much lefs in the Dia- 
meter as the Horfe draws nearer to the Center, the difficulty of 
drawing, were it not for the twifting of the Horfe, would always 
be the fame) not confidering the Strain put upon the Horfe ; or 
when by Pra&ice they have found how much a Horfe may eafily 
draw, with all the Difadvantages which the fudden turning gives 
Mm, they won't take the Advantage which more Room might 
give in removing that Difficulty, becaufe they don't care to go 
out of the Way which they have been accuftcmed to. But fuch 
Mill-wrights, as have worked at Coal-pits and Mines know -better,, 
as. they have been us'd to large Horfe-walks in Coal Fields, &c.. 



I HAVE 




I have often found that five Men are equal in Strength to one Led. IV. 
Horfe, * and can with the fame Eafe pufh round the Horizontal 
Beam in a 4 ; Foot Walk j but three of the fame Men will pufh* Antle 6 * 
round a Beam in a 19 Foot Walk, which an Horfe (otherwife e~ 
qual to five Men) can but draw round. 

-The worft way of applying the Force of a Horfe is to make 
Mm carry or draw up Hill; for if the Hill be fteep, three Men 
will do more than a Horfe, each Man will climb up fafter carrying 
xoo ft Weight, than a Horfe that is. loaded with 300 ib. This 
is owing to the Pofition of the Parts of a Man's Body, which are 
better adapted to climb than thofe of a Horfe. 

It follows from this Obfervation, that thofe who have thought 
to gain great Advantage from the Weight of a Horfe by applying 
it to an Engine to work the Forcers of Pumps, have not in the 
Execution found what they expe&ed from a Calculation of the 
Weight of that Animal, becaufe at every Step the Horfe is really 
climbing lip Hill. 

A s a Horfe from the Structure of his Body can exert moft 
Force in drawing horizontally in a ftraitLine, a Man can exert 
leaft Force that way; as for Example, if a Man weighing 140 ife 
walking by a River or Canal fide, draws along a Boat or Barge 
by means of a Rope coming over his Shoulders, or any how fafl> 
ned to his Body, he cannot draw above 27 ife, or about the feventh 
part only of what a Horfe can draw in that Cafe ; for the whole Force 
that a Man exerts in that A Orion intirely depends upon his W eighty 
and not his whole Weight neither, only about x * parts of his 
Weight, acting obliquely too, pulhing him forwards as he ftoops, 
produce the whole Force whereby the Man draws the Barge along, 
as has been demonftrated by Mr. De la Hire in a Memoire which 
he prefented to the Royal Academy of Sciences at Taris, in the 
Year 16^ \ of which I have given a Tranflation in my Notes, -j-f Ann. & 

His other Reafoning about the Application of the Force of a 
Man is juft; but his 'Data not being true, fome of his Conclu- 
fions tho' truly drawn from his "Data, are not true in Fa£t ; there- 
fore I have in the fame Note given Remarks upon what he has 
faid. 

I i 2 Ik 




A Courfe of Experimental Pbilofophy, 

Led. IV. 

In drawing a Barge in the manner above-mentioned, a heavy 
Man (provided he be not unwieldy) will do more than another* 
unlefs he carried Weight proportionably, and the higher the Weight 
is carried, the better* 

hen a Man turns an horizontal Roller or Windlals by a 
Handle or Winch, he JOhould not have above 30 lb Weight afting 
againft him, if he is to work ten Hours a Day, and raife the 
Weight about 3 Foot and an half in a Second, which is the com- 
mon Velocity that a Horfe draws with. I fay 30 tb, fuppofi'ng 
the Semidiameter of the Windlafs equal to the Diftance from the 
Center to the Elbow of the Handle j for if there be a Mechanical 
Advantage, as there ufually is, by having the Diameter of the Ax- 
el, on which the.Rope winds, four or five times lefs than the Dia- 
meter of the Circle defcrib'd by the Hand, then may the Weight 
(taking in alio the Refiftance on account of the Friaion and Stiff- 
nefs of the Rope) be four or five times greater than 30 lb, that is, 
fo much as it rifes flower than the Hand moves. 

I n this Operation the Effe£t of a Man r s Force varies in every 
part of the Circle defcrib'd by the Handle, The greateft Force is 
when a Man pulls the Handle upwards from about the Height of 
bis Knees, and the leaft Force when (the Handle being at top) a 
Man thrufts from him horizontally ; then again, the Effeft becomes 
greater as a Man lays on his Weight to pufh down the Handle ; 
but that A£Hon cannot be To great as when a Man pulls up, be- 
eaufe he can lay on no more than the whole Weight of his Body, 
whereas in pulling he can exert- his whole Strength : Laftly,a Man has 
but fmall Force to pull the Handle horizontally towards him when it 
is at loweli Let us, as Monf. de la Hire does,, fuppofe a 'Man of 
moderate Strength ; to weigh 1 40 ft, he may m the four prin- 
cipal Places of pufhing and pulling in the whole Circumference of 
Motion exert the following Forces, viz,, in the ftrongeft Point a 
Force equal to *6o it> ; in the weakeft, a Force equal to '2 y 'lis 1 in. 
the next ftrong Point, t 30 ib ; "and in the laft or fecond weak Point, 
go flb. Let us add all thefe Forces together, which will, make ^47, 
and divide them by j, and we fhall have 86 ft % and this gives us 
the 'Weight that a Man might lift by a Winch, if he could exert 
his whole Force continually without flopping to take Breath but 
as, that cannot be^ the Weight muft return and over-power at the 

firfi 



A Courje of Experimental Philofophy. 24 c 

firft weak Point, efpecially when the Handle moves flowly, as it Left IV 
muft if a Man was to exert his whole Strength all round. Be-v^v-xJ 
fides, for raifing fuch a Weight we muft fuppofe the Man to act 
always along the Tangent of the Circle of the Motion, which 
does not happen in the Operation. Then tliere muft be a fufficient 
Velocity given, ' * that the Force applied at the ftrong Points may* A 
not be fpent before the Hand comes to the weak ones, fo that it " 9 * 
is difficult for a Man to continue that irregular Motion ; and there- 
fore when there are no other Advanges, the Refiftance ought to 
be but 30 lb ; and even that could not be fupported at the weak- 
eft _ Point, were it not for the Force remaining from the ftrong 
Point. 

If two Men work at the End of a Roller or Windlafs to draw 
up Coals or Ore from a Mine, or Water out of a Well, they may 
more eafily draw up 70 ib (ftill fuppofing the Weight and Power 
to have equal Velocities) than one Man can 50 ft, provided the 
Elbow of one of the Handles be at right Angles to the other; for 
then one Man will aft at the ftrong Point, when the other ads at 
the weak Point of his Revolution ; by which means the two Men 
will mutually and fucceffively help one another. The common way 
is to put ontheHandles oppofite to one another,which cannot give the 
Advantage above-mentioned ; tho' there is fome little Force gain'd 
even in that Pofition, becaufe one Man pulling while the other 
thrufts, works at the ftrongeft of the two weak Points, whilft the 
other works at the weaker! , and fo helps him a little. 

There is indeed a Way to make a Man do a third part more: 
Work with a Windlafs when the Motion is pretty quick, as about 
4 or 5 Foot in a fecond, f and that is by the, Application of a Fly J Ann. p 
which is a Crofs with Leaden Weights at its Ends, or rather (what 
is much better) a heavy Wheel at right Angles, to the Axis of the 
Windlafs or Roller. By this means, the Force of the Power, which, 
the Man would lofe, is kept in the Fly and equally diftributed in 
all the Parts of the Revolution ; fo that for a little while a Man, 
may ad with the Force of 80 ft, that is, overcome a continual, 
Refiftance of 80 ft ;. and work a whole Day when the Refiftance: 
is. but 40 ft., 

When; 

ft The, Fly may he applied to fever al Sorts of Engines whether mo'v'd by Men, Horfes^-jfrind' 
ar Water, or any animate, or inanimate -Bower ; and is of great Ufe in- thofe Parts of an Engine, 

<vjnicks 



2j\6 A Cmrfi of Experimental Philofb 



Led. IV. When a Man carries a Weight or a Burthen upon his Back, he ex- 
erts a great Force very effectually, ' many Mufcles at once being 
employed in that Operation ; the Mufcles of his Neck, Back and 
Loyns keep his Body and Head in the proper Pofition to fuftain the 
Weight - , thofe of his Shoulders and Arms help to keep it in its 
Place; and the Mufcles of the Legs and Thighs raife the Weights 
of all the Body and Burthen as the Man walks along. In this 
way of working, three Men do much more than an Horfe, and two 
oftentimes do as much, nay even more, as may be obleiVd in 

* Ann. ip. the daily Labour of the London Porters. * A Porter will 
carry 200 1b, and walk at the rate of three Miles an Hour: A 
Goal-heaver or Porter that carries Coals, will carry a 5c ft, but 
then he does not go very far before he lays down his Burthen; 
tho 7 on the other hand he will often go up flairs with that 
Weight: Chairmen do not a£fc with all the very fame Mufcles as 
Porters, but as they have Straps brought down from their Shoul- 
ders to the Poles of the Chair, the Mufcles of the Loins and Back 
are concerned, and like wife the Extenfors of the Legs and Thighs : 
Two of them will walk very faft with 300 ife (that is 150 ib each) 
at leaft at the rate of four Miles per Hour. Whereas a Carrier's 

^ Horfe,- 

which have a quick circular Motion, and where the Power or the Refiftance acl unequally in the 
different parts of a Revolution. This has made fome People fancy thai the Fly adds a new Power ; 
fuppofing that a Fly join.d to an Engine that is to move round does help to carry it about. But th<? 
it ?nay be faid in fome way to facilitate the Motion, by reafon that it makes it more uniform and e- 
qual, yet upon the whole it caufes a Lofs of Power, and ?iot Increafe. For firfi, It requires a conti- 
nual Supply of Power to put the Fly in Motion to a certain Degree of Velocity, and to keep and main- 
tain it in that Velocity ; for that the Fly has no Motion of its own, but what it receives from the im- 
preftd Force. Secondly, The rubbing and wearing of the Pivots or Gudgeons of the Axis do fill hin- 
der and lofe the irnprefs^d Motion : And thirdly, The Air thro* which the Weights at the Ends of the 
Fly do move, do alfo hinder the Motion thro' it ( tho* lefs when the Fly is circular J and both thefe Im- 
pediments together, if the Fly be not fill fupplied with new Power, will make it ftand fill and be 
at Reft: 

So that the Fly can of it f elf add no new Power to the Motion of the Engine to which it is applied \ 
more than what is received from the firft Mover that impreffd the Motion on it, but lofes even fome 
of the firfi Motion. 

But the reafon how it becomes convenient and ufeful in many Engines (as we have fhewn in the 
Windlafs or horizontal Axis in Peritrocliio) is this* That, whereas either the Powers exerted 

hy the Engine are intermitted or unequal, and fo the Motion is more difficult in one part of the Revo- 
lution than another, or perhaps the Strength of the Man, or any other Power to he fupplied, cannot be 
fo well applied to one part of the Revolution as it can to another : In thefe Cafes the Fly becotnes a 
Moderator, and makes the Motion of Revolution almofi every where equal, tho* the Refinances are un- 
equal, and the Forces imprefd are unequal ; for that it has accumulated in it f elf a great Degree of 
Power, which it equally and 'gradually exerts, a?td as equally and gradually \ receives ; whence ma- 
king the Revolution in all fiffirts pretty near uniform, it becomes more pleafant, eafy, and convenient 
to be acled and mov*d by the impelling Force ; which is the whole Benefit which is procured by this Me- 
chanical Engine, this way applied. But I Jhall fpeak of the Fly and fome other of its Ufes in 
another Place. 



A Courfe of Experimental Philqfiphj, 2^7 

Horfe, that goes but about 2 Miles per Hour, carries only 2 24. ft ;Le£h IV, 
or fometimes, when the Roads are very good, and the HorfesU^V^j 

firong, * 270 lb* * Ann. 11, 

Mr* Richard New/ham Engineer of Cloth-Fair max Smith fie li^ 
has contrived his Engines to put out Fires in fuch a manner, that 
part of the Men that work them exert their Force by treading^ 
which is more effe£tual than an^ other way that Men can work at fuch 
Engines, the whole Weight of the Body being fucceffively thrown 
on the Forcers of the Pumps ; and even part of a Man's Strength 
may be added to the "Weight by means of horizontal Pieces to which 
he can apply his Hands when he is treading : Whereas, by apply- 
ing the Hands to move Leavers or turn Winches, the Power mult 
a£t very unequally : This is the Reafon why with the fame Number 
of Men he has generally thrown Water farther, higher, and in great- 
er Quantities^ with the fame fiz'd Engines, than other Engineers* 
who have try *d their Engines againft his. 

N.B. His Engines have fever al Conveniencies peculiar to 
thern r which makes them preferable to all others that I ever 
faw> for extinguijhing accidental Fires ; but I referve their 
^Defcription for another part of my Book, 

THElaft and moft effectual way of aMatfs working, is the A£fci~ 
on of rowings wherein a Man a£ts with more Mufcles at once for 
overcoming the Refiftance, than in any other Pofition; and as he 
pulls backwards the Weight of his Body affifts by way of Leaver*. 

CO ROLLOUT* 

Prom the Confideration of the feveral Ways of aMan 9 s a£Hng m. 
the way of Labour,, compared with the laft, we may fee how much* 
People are miftaken who think to row a Galley,Boat, or Barge,by ver- 
tical Oars fixM on a horizontal Axis like a Mill- Wheel, the Mem 
working this Machine by heaving at a Capftane ; or turning Winches* 
within the VefTeL For this will always be bringing the Men 
from eafier and more effectual, to harder and lefs advantageous* 
Work ; as has been found by a great many more Enginers than will 
own it, and will be found by all that fhall ever try it, be the Ma- 
chine made in any Shape whatever^ unlefs whgn the. Men work in a 
rowing Pofture* 

A PRO- 



A Courfe of Experimental 




* Ann. 7« 



Led. IV. A prodigious Force may be exerted by the Mufcles of the 
o*v^> Legs and Thighs to raife an immenfe Weight a fmall Height • but 
as that Operation cannot be continued and brought to daily La- 
bour, I refer the curious Reader to the Notes where that is more 
fully explain d : * neither do I here take notice of digging, ham- 
mering cleaving of Wood, or any of the laborious Rations 
of Handy-craft Trades ; becaufe fqme Men are much more dextrous 
than others; and the fame Man by long Ufe becomes fo per- 
f eft m one way of working, that by an acquir'd Sleight he fhall do 
twice the Work that an unexperienc'd Perfon can do, and vet not 
employ half fo much Strength, But this is properly Craft and not 
Labour, which laft was all I meant to confider here. 




Anno- 



Annotations on Lefilure IV. 



i* TT^ AGE 184. — C *The Frittion is equal to about one third of the Annotat 
W ?ight % &c.] There are fome Cafes wherein the Friftion does not Left IV 
come up to a third Part of the Weight of the Body which rubs j ^r\f^ 
but as in moft Cafes it does, I chofe to give that Proportion as the Founda- 
tion of the Calculation of the Fri&ion of an Engine composed of many 
Parts before we ere& it, efpecially in regard to the Manufadures, becaufe the 
wearing of the Parts of Machines will in time alter their Figure and en- 
creafe the Friftion, And it will be better in Pra£Hce to find the Friftion 
to be lefs than in the Theory, tho' that feldom happens, when calculated 
from a third of the Weight. 

2. CPage 186. // would require one third of the Weight of the Skdge r 

&c-3 In the Table of the Friftions of Sledges (Page 193, 194 and 195) 
quoted from Monf. Camus's Experiments made on fmall Models, there are 
more Cafes wherein the Friftion is left, than where it is more, than one 
third of the Weight 5 but it is to be oblerv'd, that in all his Experiments 
the Sledge is in Motion % but as 1 mentioned in my laft Note, I rather 
chofe to continue the Proportion of a third on account of Accidents, be- 
ginning to draw from Reft, [and meeting with Rubs and Unevennels in the 
Streets, &c. 

3. C? a g e 20 *• — We cannot expeU that any Carriage to hear Weight 
can have fo little Frittion^ &c. —the manner of remedying FriSiion^ &c/j 
If the Axels in fome Carriages being made of Iron* and in others only 
clouted (that is cover'd) with Iron, were to run in brafs Boxes fix'd in the 
Naves of the Wheels, they would go lb much eafier, and wear fo much longer,, 
without danger of firing, as to make full Amends for the extraordinary Ex« 
pence. Where People are curious and don't value Cofty as in Chaifes and 
ibme Chariots, an Iron Axel being left in Diameter will have lefsFri&km in 
proportion as it is fmalkr, and laft very Jong if it turns in Boxes of caft 
■Brals-, but the Gudgeon in the Box xnuft.be fufficiently Jong, which it 
may be without encreafing the Friflion, as has been already pro? 9 d | but' 
will be more clearly evinced by Experiments made on a Machine which I 
fhall defcribe in this Annotation, If the Gudgeons are but two or three 

k Inches 




Annotat. Inches long as fome have made them, thinking thereby to diminilh the 

t&Q:. IVVFri&ion, they will only wear two or three times fafter than if they had 

|/YV been made four or fix Inches long, 

A' Wheel of an Engine whofe Axis is fix'd to, and turns with, the 
Wheel, may have the Fri&ion of its Gudgeons diminifh'd in any Propor- 

|PL lS.F.d.tion. As for Example, under the Iron Gudgeon G g, f which we will 
fuppofe here of an Inch in Diameter, let there be two brafs Rollers AB 
of eight Inches Diameter each, whofe Axes C, D, are horizontal and pa- 
rallel to the Axis of the Wheel : the Rollers which confequently are ver- 

tPl,i8.F.7.tical (as may be feen in Fig. 7. *|-) are about an Inch thick (or more if 
you will) and not in the fame Plane, but one a little before the other, 
and parallel to it. Upon thefe Rollers is fupported and turns the Gud- 
geon Gg df the great Wheel. In this Cafe the Friftion of the Gudgeon be- 
comes eight times lefs than if it mov\d in the common Braffes \ for if we fup- 
poie the Gudgeon to move in the Direction Gg, it will not quit the Part 
g of the Wheel A on which it bears, to go to another bearing with its 
touching Part, as happens when it turns and makes a Fri&ion in the com- 
mon way, but it brings along with it the Circumference of the Wheel or 
Roller A, turning it about in the Dire&ion A g, whiift its other touching 
Part G in its turning does alfo carry round the Roller B in the Dire&ion 
G B, and thefe Rollers wou'd follow that Motion without any Friction, 
were it not for the bearing of their own Iron Axes C, D, in their Braffes. 
So that the Fri&ion is transferred from the Gudgeon Gg to the Axes C, D, 
where the Velocity of the rubbing Parts being eight times flower than it 
wou'd have been at Gg, the Friftion muft be eight times lefs, as we have 

\ Page ihewn already. Now tho' thefe Rollers have four bearing Points, and the 
186. ' other two which fapport the Gudgeon of the great Wheel's Axis have 
alfo four bearing Points, the Fri&ion is no greater, than if there was but 
one bearing, becaufe each of thele Points fuftains but an eighth part of 
the Weight, ^therefore the Friffiion is made eight times lefs by means of thefe 
Rollers : which was to be provd. 

S C H 0 L I V M. 

If the Axes of the Rollers are made but of half the Diameter of the 
Gudgeon, as at E and F, then the Friftion will be 16 times lefs 5 and 
yet they will be fufficiently ftrong$ for as a Cylinder of half an Inch 
Diameter is equal in Strength to the fourth part of one of an Inch, the four 
Ends of the Axis of two Rollers at one End will be equal in Strength to 
the Gudgeon, and £6 at the other End. 

C O R O h LA R r. 

Hence follows, that if the Ends of the Axes of the Rollers were each 
of them fiipported by two other fuch Rollers, the Fri&ion would again be 
diminilhed 16 times more. Let us for Example luppofe a Wheel to be fix 

Foot 





xperimental 



Foot in Diameter and to weigh 64S jfr, the third of that Weight for Annotat 
Friftion is 216%, which muft be divided by 72, becaufe the Diameter of Led. I\T f 
the Gudgeon is fo many times contained in the Diameter of the Wheel,- {j^\r\j 
and we fliall have 3 lb for the Friftion of the Wheel upon common BralTes 5 
but this Number muft be divided by 16 times i6 y that is, by 255, on' 
account of the Rollers bearing on Rollers, which will thus reduce the 
Friction to ~ ~h f or little more than one 85 th part of a Pound, or 3 
Drams of 16 to the Ounce, 

4. [Page 217. FriBion on the Axel^ &c] Since, as we have laid 

and already provM % the Fri&ion arifes from the Weight that preffes the* £ ( 
Parts together, and not from the Number of Parts that touch % there is no 184, 
Occafion for ihortening the Axes of Wheels, either in Carriages or any 
other kind of Whe«is in order to diminifli the Fri&ion ; for that will not 
only fail of the defir'd End, but make the rubbing Axis wear out much 
fafterj and in Clock-work it is of bad Conlequence, becaufe when the 
Holes are counter-funk to ftiorten the bearing, the Holes fbon wear too big t 
whereas, if they were made only cylindrical the thicknefs of the Frame-* 
Plate, the Fri£tion wou'd be no more, and the Pivots wou'd wear much 
longer } and indeed it is now what ail good Clock-makers pra&ife \ for if 
they counter- fink, it is but a fmall Depth to hold Oil. Experiments oft 
the following Machine will make this more fenfible and evident. 

Plate Fig. 8* 

On the flat bpfs Plate ABC (which,. is here reprefeated almoft as big 
as the Machine) are fix'd two upright Plates D and E, with a Slit in one 
of them at D, and a Hole in the other between the Letters K and L, to 
receive the fmall Pivots at the Ends of the Axis D K of the ^Wheels 
ZFLG. But thofe Pivots, which are but about one 30th of an Inch in 
Diameter, do not bear on the Hole at K and the bottom of the Slit at D § 
for they are fupported upon two circular Plates or Rollers at each End of 
the Axis, viz. the vertical Plates M 1, M 2, M 3, M 4, in the manner 
defcrib'd in the laft Note, and reprefented at Gg Fig. <5. f and the Sefti- 1 PI. 1 8. E 
on of one of the Rollers or Plates is Ihewn by Fig. j. So that when the 7. 
Wheel turns round one way, all the rolling Plates turn the contrary way as 
freely as if the Pivot had been a Pinion, and the Wheels or Plates had heen 
tooth'd, becauie the Axes of the Plates have very fmall Pivots which turn 
in very fhiooth Holes, that are made andpoliih'd in the four upright fix'd 
Plates or Cocks Ni, N2, O and P, which laft Cock has only the Corner of I 
its Bafis vifible in the Figure, the Wheel M % hiding it in this Situation 
of the Machine. The little Cocks, fuch as D, d 7 ferve for the Ends 
of the Pivots to bear againft (both for the great Wheel and the four lit- 
tle Wheels, there being ten of them of which only three are vifible here) 
and by that Refinance againft the Ends, the Shoulders as 'C.C, Fig. 7. ^*-pi. i8 .F.7 
will -never, rob at ail. ^ 

k 1 B 




Annotat By this means the great Wheel has fo little Friftion, that if we apply 
Xe£t. IV* a Finger to its Circumference to put it briskly in Motion, any Point of 
i^yNj its Circumference will go more than the fpace of & Mile before the Wheel 
ftopsi for tho' one cannot count the Number of Revolutions of the great 
Wheel by looking at it, yet one may know their Number by looking at 
the Holes which are left in the fmail Wheels (one in each) for that Pur- 
pofe i for they being two Inches Diameter tijrn but once whilflr the great 
Wheel (whole Pivots gives them Motion) turns fixty times. 

The Fri&ion of the great Wheel thus becoming fo little, as to be in a 
manner infenfible, it is fit for the Purpofe intended. Then on the top of 
the Cock or upright Piece Q R, fcrew'd down faft by its Baft or Foot Q_, 
is faften'd by a Screw at R one End of the Spiral Spring S x, S 2, 83, 84, 
whofe other End is faften'd to the Axis of the great Wheel near S 4, 
Now if the Wheel be made to turn on its Pivots, by Jbringing the Point Z 
of its Circumference towards the Index Y, which points to Degrees on 
the Edge of the Wheel (but not reprefented here except by the Dots 
mark'd from Z towards Y) as foon as we let it go it will return towards Z 
and make feveral Vibrations backwards and forwards, like the Balance of a 
Watch, for a long time-, but if any thing bears againft the Axis HID, 
which is truly cylindrical and one 4th of an Inch Diameter, then there will 
be fewer Vibrations in proportion to that Fri&ion. Now to fhew that the 
Fri&ion is proportional to the Weight that preffes on the Axis, and not the 
Surface, the following Experiments are made* 

Experiment I. 

f FLxS.F.9* Take the Piece of Figure 9 *f* weighing half an Ounce (being made in 
the Form of a flat Crofs, and after filing, ground fmooth upon an Oil-ftone 
on the flat Under-fide of V, with a little Hole at the End T, and a fmail fo- 
lid round Piece hanging down at the oppofite End X) and lay it over the 
Axis of the Wheel betwixt I and D, fo that the Weight of the hanging 
End X, drawing down the flat V upon the faid Axis, makes the End T rife 
with its little Hole againft the Point or lower End of the Screw T of the 
Cock /T, which keeps it in its Place when the Axis turns round under it ; 
then having brought Z to Y, or drawn back that Point againft the Bent of 
the Spring about 90 Degrees, obferve the Number of Vibrations that the 
Wheel makes before it ftands ftill by the Fri&ion of the Crofs in the Situa- 
^PU8.F.8,t:ion reprefented by faint Lines, at TVX Fig. S. * Suppofe the Mum- 
f Pl 0 ia,F.j[O,ber of the Vibrations be 505 then the Crofs ©f Fig. 10. *f be put on in 
the lame manner and at the fame time juft by the other, and kept in its 
Place by the bottom of the other Screw / 5 as it is exa&ly the fame in Fi- 
gure and Weight as the firft Crofs, it will add as much more to the Friftion 
of the Axis, the Weight preffing as well as the Surface rubbing being dou- 
bled j which appears by giving Motion to the Wheel as before, becaufe 
then the Number of Vibrations will be but 25* 

Exp R-> 



A Courfe of Experiment at Philofophy. 253 



Ex pekiment II. Annotat* 
Inftead of the two Crofles abovementioned, put on the Croft of Fig. i^Left. IV, 
* which weighs one Ounce (that is as much as the two others) but has^^'^v^ 4 
the Surface under V exaftly fmooth'd and polifli'd like the others: Then * 91 u 
put the Wheel in Motion as before, and the Vibrations will be but 25 in 
Number, tho* the Surface rubbing is but half, becaufe the Weight is the 
lame. And this is further prov'd * 



Experiment III. 

In which, the Piede X muft be unferew'd from its Place and fcrew'd a- 
gain in the fame Hole on the other fide of the Crofs to bring the little Flat 
of the Prim at V to bear upon the Axis of the great Wheel inftead of the 
broad Part of the Crofs. Then alfo will the Wheel lofe its Motion after 
25 Vibrations, tho' the bearing Surface be above twenty times left than 
when both the firft Crofles were on > becauie the Weight is the fame. 

5- D? a S e 232. ~ — -Jhoifd alter the manner of working, &c. inftead of 

gaining an Advantage he mufi call in more Men to perform the JVorL - 

Some have endeavoured to render this Engine more ufeful by caufing it 
to roll upon an inclined Plane, inftead of making it rife direftly up in the 
manner delcrib'd, and condemned in my Account of it. I thought proper 
to fliew here, wh^t muft be the Lofs of the Power in proportion to the 
Inclination of the Plane. 

I lay therefore, "That in every Inclination of the Plane, if the Sine of 
the Angle of Inclination be t&ken in Parts of the Radius of the Axel> or 
Roller, The Power will be to the freight ; J as the Radius of the Roller -}r- 
the Sine of Inclination: to the Radius of the Wheel, — -the faid Sine of 
Inclination; that is, in the Fig. P ( = 1) :'W ( = 3) :;dk: ak. t P1,ij».F-i« 

1 p. Fig. 1. . 

In the prefent Experiment B E is an inclined Plane, on which the Roll- 
er C is to roll up, touching the faid Plane at the Point c\ AM is the 
Wheel behind that Plane another fuch Plane, and equally inclin'd, being 
alfo fuppos'd behind the Wheel, to fupport the other End of the Roller. 

The Lines of Direftion of the Power and Weight being a? and dVi % 
through the Point of Contaft or Center of Motion c, draw AD parallel 
to the Horizon, and perpendicular to a? and iWs through the Center 
of the Engine C, draw a d parallel to A D. Suppofe the Angle B e A of 
the Plane's Inclination to be 30 0 , the right Sine will then be equal to half 
the Radius ^ therefore dividing C 2 (the Radius of the Roller) into two 
equal parts at k, if you draw kc and C c, the Angle kcC will be equal 
to B*A, and its Sine will be C*. Now fince it is evidently the fame 
thing to make ufe of a d for a Lever, whofe Center of Motion is at *, 
as of A D equal and parallel to it with its Center of Motion at c : it 
follows, that, in this Inclination of the Plane, theDiftanceof the Weight 

dk is greater than dC (the Diftance of the Weight in the common Ufe of 

■ - ■ this 








ourje oj iLxpertmenia 



Annotat. this Engine) by the Addition of this Quantity €£, the Sine of the Angle 
Le£t, IV. of Inclination ^ and ka 7 the Diftance of the Power is lefs than Ca (the 
- — - Diftance of the Power in the common way) by the Subtraaion of the 
faid Quantity or Sine C k : confequently th^t on an inclined Plane j the Pow- 
er is to the Weight ; ; as D*: to c A. $L E.D. 

C O R 0 L LA R T I. 

Hence it follows, that the Radius of the Wheel, and the Radius of 
the Roller being given, the Lofs of Power may be found in any Inclina- 
tion of the Plane. Thus, as here the Power, which in the common way 
wou'd be but one 5th of the Weight, muft be one 3d part of it : So if the 
Angle of the Plane's Inclination was but n° 32', thePowtr wou'd be one 
4th of the Weight , &c. 

COROLLARY II 

Hence follows alfo, that if the Plane BE be horizontal, no Force of 
the Power will be loft, becaufe eg: cf\\ CG: CF. 

SCHOLIUM. 

As the Friaion of the winding of the Ropes, fuch as B c in the new 
Way,Js greater than the Friaion of the Pivot in the old Way (befides 
the Friaion of the CoHara of the Counterpoife to the Engine) fo that 
Friaion diminiihes, as the Ropes bear lefs Weight, according to the Di- 
minution of the Angle of the Plane s and when the Plane is horizontal, 
and without a Counterpoife, even then the winding up of the Ropes, and 
Preffure of the Roller againft the Plane^ is equal to the Friaion in the 
common way. 

N. B. / made the Experiment with Pivots twelve times lefs in Diame- 
ter than the Roller ', and fine pliable Silk infiead of Ropes. 

6. P?age 243. « Five Men are equal in Strength to one Horfe, &c] Such 

Englijh Authors as have compared together the Strength of Men and 
Horfes at a Capftane have found their Forces to be in that proportion, 
as Sir Jonas Mogre and others, But the French Authors always 

make an Horfe equal to feven Men y which I believe to be according to 
their Obfervations. Nay, and I have obferv'd the Labourers in Holland (one 
with another) to work with a Force pretty near in that Proportion, So 
that we may fay, — That five Englijh Labourers are equal to an Horfe, and 
only feven French Men or as many Dutch Men. But here we do not at all 
confider Skill, or Sleight, which make a Man of the fame Strength do 
much more than another. But in Turkey* the Porters will carry twice 
more than the ftrongeft Englijh Porters, as we ftail more particularly confider 
in the next Note. 

7. [Page 



ACourfe of Experimental Philofophy. 255 



7, [Page 248. — a 'prodigious Force may he exerted, &cj About 30 Years j^ nja0 ( at 
ago one Joyce, a Kentijb Man, famous for his great Strength (tho* not| rj. Ty- 
quite lb ftrong as the King of Poland Joy the Accounts we have of that Prince) 
ihew'd feveral Feats in London and the Country, which fb much fiirpri^'d^^^^ 
the Spectators, that he was by moft People caiPd the fecond Sampfon ^ 
but tho' the Poftures which he had learn'd to put his Body into, and found 
out by Practice without any mechanical Theory, were fuch as would make 
a Man of common Strength do fuch Feats as would appear furprizing to 
every body that did not know the Advantage of thole Pofitions of the 
Body } yet no body then attempted to draw againft Horfes, or raife great 
Weights, or to do any other thing in Imitation of him j becaufe, as he was 
very ftrong in the Arms, and gralp'd thole that try'd his Strength that way 
fo hard, that they were obliged immediately to defire him to defift, his 
other Feats (wherein his manner of a&ing was chiefly owing to the me- 
chanical Advantage gain'd by the Pofition of his Body) were intirely at- 
tributed to his extraordinary Strength. 

But when he had been gone out of England, or had ceafed to fhew his 
Performances, for eight or ten Years-, Men of ordinary Strength found out 
the Way of making fuch Advantage of the fame Poftures as Joyce had put 
himfelf into, as to pals for Men of more than common Strength, by 
drawing againft Horles, breaking Ropes, lifting vaft Weights, &c. (tho* 
they coifd in none of the Poftures really perform fb much as Joyce; yet 
they did enough to amaze and amufe and get a great deal of Money) lb 
that every two or three Years we had a new fecond Sampfon. 

About 1 5 Years ago a German of middle Size, and but ordinary Strength, 
fhew'd himlelf at the Blue Pofts in the Hay Market, and by the Contri- 
vances abovementioned, pafs'd for a Man of uncommon Strength, and got 
confiderable Sums of Money by the daily Conconrfe of Spe&ators. Af- 
ter having leen him once, I gueiVd at his manner of impofing up- 
on the Multitude i and being *efolved to be fully fatisfied in the Matter, 
I took four very curious Perfons with me to lee him again, viz. the Lord 
Marquis of "TuUibardin, Dr. Alexander Stuart, Dr. Pringle, and a me- 
chanical Workman, who us'd to affift me in my Courles of Experiments. 
We plac'd our felves in fuch manner round the Operator as to be able to 
oblerve nicely all that he did, and found it fo pra&icable, that we per- 
formed feveral of his Feats that Evening by our felves, and afterwards I 
did moft of the reft as fbon as I had a Frame made to fit in to draw, and 
another to ftand in and lift great Weights, together with a proper Girdle and 
Hooks. I likewile fhew'd fbme of the Experiments before the Royal Society ^ 
and ever fince, at my Experimental Le£lures, I explain the Reafon of fuch 
Performances, and take any Perlbn of ordinary Strength that has a mind to 
try, who can eafily do all that the German abovemention'd us'd to do, without 
any Danger or extraordinary {training, by making ufe of my Apparatus for 
that Purpole. I don't hear that any of thele Sampfons have attempted fmc€ 
to impale upon People in the fame manner in or near London* 

But 



2 $6- A Courfe of Experimental Philofophy. 

Annotat. But now it will not be improper to mention what were the Feats of 
Left. IV. Strength which the German us'd to perform (for I never law Joyce) and to 
w-v-n^ fliew, from the Make of the human Body, how eafily any one may do the 

Is inc. 

ift, The ftrong Man IHL on the Frame AGBEFCD fat upon an 
* PI. 19. F.i. horizontal Board, or rather inclining backwards as FG,* with his Feet 
againft an upright immoveable Prop as DCF coimterbrae'd at E, with a 
ftrong Girdle H round him a little below his Hips ; to the Iron Rings of 
which Girdle was faften'd a Rope by means of a Hook. The Rope went 
between his Legs and thro 5 a Slit of the Prop at L, and feveral Men at 
M N, or two Horfes could not by their pulling, move him out of his 
Place. 

N.B. His Hands at K feem'd to pull, but were ef no Advantage to him : 
nay had he lifted the Rope ever fo little with them, it would have been a 
Difadvaniage : and tho r the Board on which he fat was (when I faw 
him) in the horizontal Pofition L P, it is much better and lefs dangerous 
to have it inclined as FG, and only an Hole at L for the Rope to run 
thro" inflead of an opening from L up to D, as I fhall fhew in explaining 
this Operation. 

t.Pl.ip.F.3, 2 dly, The fame Man IHL f having fix'd the Rope abovementioned 
round a ftrong Poft at R, and then pafs'd it thro' a fix'd Iron Eye at L, 
fix'd it to his Girdle, and letting his Feet againft the Poft near the faidEye 
rais'd himfelf from the Ground by the laid Rope, which he broke by 
fuddenly ftretching out his Legs and fell backwards- on a Feather Bed at 
B laid on the Ground to catch him that his Fall might not hurt him. 

*P1.ij.R4. ^ idly, He lay down on the Ground in the Pofture IHL # with an An- 
vil KH on his Breaft at H, upon which another Man M hammered with 
all his Force the Iron K with a Sledge Hammer * and fometimes two 
Smiths ait a great cold Iron Bar in two with Chizzels. Sometimes a 
great Stone of which the half is feen at S was laid upon his Belly and 
broke with a Blow of the great Hammer. But he had the Stone broke 
upon his Belly in the Pofture of Fig. 5. which is much lels dangerous 
when nothing is under the Back, than when a Man lies upon folid Ground^ 
as we fliall ihew. 

^thly, The pretended Sampfon puts his Shoulders (not his Head as he 
us'd to give out) upon one Chair and his Heels upon another, and fup- 
ports one or two Men {landing upon his Belly, railing them up and down 
as he breathes, making with his Back-bone and Thighs and Legs the Arch 
~f PI. 19.F.5JH L, whole Abutments are at I and L. 

N.B. The Stone of one and a half Foot long, one Foot broad, and five or 
fix Inches thick, is laid on at H when it is to be broken by a Blow of a 
Hammer. 

'■♦Pl.19.R6. ^thly, He lies down on the Ground in the Pofture IHL* and the 
Man M (landing upon his Knees, he draws' his Heels towards 
his Breech and fo raifes his Knees overC, and lifts up the Man gradually, 
till having brought perpendicularly under the Man as in Fig. 7. he raifes 



A Courje of Experimental Thihjophy. 257 

his own Body up, and putting his Arms about the Man's Legs rifes with Anhotat. 
him and lets him down on lbme low Table or Eminence about the Height Left. IY» 
of his Knees : and this he fbmetimes does with two Men *, which is no 00/"XJ 
difficult Performance. 

6thly, He ftands in the Frame A B C D E F, # and pretends to raife upj* PI 20. F.20 
but does really fuftain^ a Cannon G laid on the Scale Ss, the Ropes of 
the Scale being fix'd to a Rope or Chain LH 3 hanging at his Girdle H 2 
his Affiftant knocking away the Rollers R,r 7 from under the Scale when 
once he has fix'd himfelf lb as to have his Ropes tight and his Legs and 
Thighs quite ftreight. 

N.B. It is very near as eafy to break the Rope with the Eye L fix'd 

into the Ground or Floor by means of the Girdle H, *f« Fig* 1. as in-fPl 2Q.F.ij 
the manner reprefented in the * third Fig. of Plate 19. But he never* PL 19. F. 3. 
tried it that way \ becaufe it is fo obvious that fever al People wou'd imme- 
diately have tried it too^and'would find that there is no difficulty in breaking 
the Rope thus , as I have often done it\ but by making the Fall backwards 
feem necejfary in the Operation^ few Perfons care to try it his way* 
The 'f- 4th Figure reprefents the Girdle made of ftrong double Horle Girt, t PI* 2 <>-F-3$ 
with ftrong Iron Loops at G and R. The Hook is leen at Fig, 5 ; and4> and 2- 
the Pofition of the Iron Eye at Fig. 3, where you may obferve that the 
Edge of the Eye, and not the open part, is towards the Poft, fb that the 
Rope does not eafily flip thro 5 the Hole, but jams or flops in it, where- 
by the whole Strength of the Man's Effort a£fcs upon one part of the Rope, 
and fo it is eafily broken. 

The Man likewile us'd to take a flat Piece of Iron of the Figure mark'd 
7, # and twifl: it into a Screw. But his manner of doing it made it very* Pi. 20. F.^ 
eafy ; for he firft bent the Iron to a right Angle, as at Fig. 8 : then wrap- 8 > and 9, 
ping his Handkerchief about the broad flat upper End of the Iron, he 
held that End in his left Hand, and with his right Hand applied to the 
other End twifted about the angular Point, as in Fig. 9. 

N.B. My Lord Tullibardin took one of his Irons and did the fame 
Thing before him 5 and indeed what was harder for he untwified one of 
the Irons that the Man had twifted. 
In order to explain how the abovemention'd Feats may be performed 
by Men of no extraordinary Strength, I have in the 6th Figure "* drawn *pi >209 p, ^ 
the lower part of a Skeleton, containing lb many of the Bones of the hu- 
man Body as are concerned in thele Operations, making the Figure pretty 
large, to fliew the better how the Girdle is to be applied. 

The Bones mark'd, ISAPAI (a) which compofe the Cavity calPd the 
Pelvis, contain a bony Circle or double Arch of fuch Strength, that it 
wou'd require an immenfe Force to break them by an external Preffure di- 

LI re&ed 

(a) Thefe Bones are thus dijlinguijbed by Anatomifts. S, the Os Sacrum : II 5 /Allium: A A, 
the Os Ifchium ; nvhofe Jiro?igeJl fart has on each Side an hemifpherical Concave ' ? in which the round 
Head of the Thigh Bone is received and turns round? being held by a ftrong Ligament in its ' middle : 
thofe Parts of the Bone that join together before betwixt A A and above P are calFd the Os Pubis 
or Ofla Pubis. 



1 8 A Cow ft of Experimental Philo/bphy. 

Annotat. reded towards the Center of the Circle, or the middle of the Pelvis. It 
Le£t IV« i s aifo. to be obferv'd, that thofe Parts of this bony Circumference, which 
u/"'V"\J receive the Heads of the Thigh-bone above, at, and below A, call'd the 
Ifchium or Coxendix, are the ftrongeft of all, fb that a very great Force may 
pufh the Heads of the Thigh-bones upwards (or, which is the fame thing, 
the upper Parts of the Coxendix downwards) or towards each other in a 
lateral Dire&ion from A to A, without doing any Hurt to the human Body* 
Now if the Girdle above defcrib'd be put round the Body in the man- 
ner reprefented in the Figure, and be drawn downwards at G by a great 
Weight W, it will prefson the Os Sacrum behind, and the Ilium 5 then it 
will by its Preflure on TT the great Trochanters of the Thigh-bones 
drive the round Heads the fafter into their Sockets, fb as to make them 
\lels liable to flip out and ftrain the Ligament by a Pufh dire&ed upwards. 
So that the femicircular Part of the Girdle TCSCT preffes together the 
bony Arch denoted by the fame Letters, which, according to the nature of 
Arches, is the ftronger for that Preflure. The Abutments of the Arch 
cannot come nearer together by reafon of the Refiftance of the ftrong Bones 
A P A, neither can they fly outwards, becaufe the Girdle keeps them to- 
gether. Then the Thighs and Legs TDB are two ftrong Columns, ca- 
pable of fuftaining four or five thoufand Pounds at leaft 5 provided they 
ftand quite upright. The Mulcles here are put to no Strain, being no 
farther concern'd than to balance each other ; that is, the antagonift Mufc 
cles, Ext en/or s and Flexors only keep the Bones in their Place, which 
makes them refift like one entire Bone form'd into an Arch. 
*?iio. F.2. This fhews how eafily the Man of Fig. 2. * may iuftain a Cannon of 
two or three thoufand Pound Weight. The fame Solution will alfb ferve 
f PI.19. F. i.f° r the Refiftance of the Man of Fig. 1. Plate 19. *\ whom five Men (nay 
ten Men or two Horfes) cannot pull out of his Situation when he fits fo as to 
have his Legs and Thighs in the horizontal Line PF, or in a Line in- 
clining downwards towards A ; for then, tho 1 there is a difference in the 
fitting Pofture from the ftanding Pofture before defcrib'd, yet by reafon 
of the Mobility of the Heads of the Thigh-bones in the Acetabula or Ca- 
vities of the Coxendix, the Arch is the fame and as ftrong as before, its 
Abutments being equally fupported by the Legs and Thighs. It is only 
the bending of the Back-bone above the Girdle to bring up the Body 
which makes the difference of Pofition in the Man, tho 5 not fenfibly 
in the refitting Parts. The Impoffibility of overcoming the Refiftance of 
the Man that fits with the Girdle about him, without crufhing his Legs 
and Thighs end-wife into one another, depends upon what has been laid 
* Ann. L. in the * fifth Note of the third Le&ure (Page 1 44 ) where we have fliewn 
III. p. 144. that a Power a£ts ineffectually upon a Leaver, when it draws it againft the 
Center of Motion. This will be further explained by the 2d Fig. of Plate 
*Phi9.F. 2. rp, # where the Leaver HL, whofe Center of Motion is at L, reprefents the 
ftrong Man's Legs and Thighs, the Power of the Men or Horfes pulling at 
M, being applied at H, and drawing in the Dire&ion H L. The fame 
will happen when the Leaver is in the Pofition H L } but if the Man^fhou'd 

fit 




fit with his Breech higher than his Feet, fo as to have his Legs and Amiotafc, 
Thighs in the Pofition of the Leaver h L, Mib> the Line of DireaioiiLed. IY« 
of the Power wou'd make with the Leaver the Angle Ibh, whofe Sine u^y^SJ 
being /L wou'd reduce the Aftion of the Power to the fame Thing as if 
the Weight of the Man was fulpended at h the long Brachium of a bend- 
ed Leaver hhl, and the Power fhou'd draw at the Point /, by the fhort 
Brachium /L. Then if the Power was to the Weight in a Ratio fomething 
greater than that of h I to /L, the Man wou'd be pull'd upwards in an Arc 
whole Center is at L, his Refiftance decreafing continualJyj becaufe then 
only his Weight wou'd a£t againft the Power, by the help of a Leaver 
which in its Motion wou'd continually encreafe the aSlingDifiance of the 
Power, and diminifh that of the Weight. Now as this may happen to a 
Man fitting upon a horizontal Board, if his Girdle be a little too high ? 
or he be pull'd on the fudden, before he is rightly fix'd and his Legs 
and Thighs are i$ their due Pofition \ I wou'd always advife the Board to re- 
cline in the manner FG * to prevent fuch a Surprize, which can hard-* FI.xp.F 0 i 9 
ly happen then, becaufe the Point H muft rift quite above the Line 
LP before the Power can gain any Advantage. Nay, for greater Security, 
Inftead of the flit DL (or L / f Fig* 2.) I ufe only an Hole at L, for^pLi^F,^ 
the Rope to pafs thro', and always be between the Legs and Feet. 

I have obferv'd the pretended Strong Man fometimes to have a Ihort ftrong 
Stick of about a Foot long tied to the Rope at K, that in cafe of a Sur- 
prize, that Stick might flop againft the Props D and C 3 lb as to prevent 
his being drawn any farther forward in fuch a Cafe \ and then he held 
the Stick in his Hands, pretending to pull with his Hands to make the 
Trick appear the more ftrange. 

But in breaking the Rope the Mufcles muft a£k in extending the Legs 
and that we may the better explain that A&ion, we muft: confider a Man 
breaking the Rope as reprefented in the firft Fig. of Plate ' 20. * that way * pj a20 p Te 
being more fimple than when it is broken in manner of Fig. 3. Plate 19. -j~ ^p] s 19 'jrV 

The Rope being faften'd to a Poft at P, or any other fix'd Point, is 
brought thro' an Iron Eye L to the Hook of the Girdle H of the Man 
H I, and lb fix'd to it by a Loop, or otherwife, as to be quite tight,whilft 
the Man's Knees are fo bended as to want about an Inch of having his 
Legs and Thighs quite upright: Then if the Man on the Hidden ftretches 
his Legs and lets himfelf upright, he will with Eafe break the very lanie 
Rope which held two Horles exerting their whole Strength when they 
draw againft him 5 luch as a Cart Rope, or a Rope of near three quarters 
of an Inch Diameter, which may be broken by a Man of middling Strength, 
by the Aftion of the ten Mulcles (a) that extend the Legs, five belongs 
ing to each Leg. 

L 1 2 If 

(a) The five Mufcles that extend each Leg are defcritid bf the Anatotiiifls. Their Names are^ 
1. Membranofus arijing from the upper part of the Spine of the Os Ilium, and infer ted a little be- 
low the Knee into the outer and the forefide of the Tibia and Fibula, 2» The Re$us fpringing from 
the lower part of the Spine of Os Ilium, and infefted f alfo a little below the Knee inU the fore/Ide of 

' ■ the 




Annotat. i If the Rope is ftrong enough to bear i&oo but will break by hang- 
Led. VI- n § a litc ^ mo * Q Weight to it | two Horfes, or ten Men, cannot break it 
(v ^rsj by fair pulling or drawing againft the fitting Man. of Fig. i. Plate 19. * 
^Pl.ip.F. 1. For as an Horfe in common hard Work of fix Hours a Day can only pull 
f Page 240 ifo, t ^ e cannot draw more than double that Weight when he is 
whipp'd and exerts himlelf} fo that two Horles, or ten Men, equivalent 
to them, cannot with a J irk draw above 1000 ifo, whereas the Rope has 
been fuppos'd ftrong enough to fuftain 1800 ifo, and yet it may be broken 
*P1.2o.F. i. by an ordinary Man in the Pofture of Fig. 1. Plate 20."* Neither need 
we wonder that the Mufcles Extenfors of the Legs ftiould exert fo much 
Force, when we confider their Bigneft and Length-, efpecially if we com- 
pare them with the fourMufcles that pull up the lower Jaw-bone (which tho' 
they all four do not weigh a Pound) yet enable fbme Men to crack an A- 
pricock or a Peach-ftone, which could not be broken without an immenfe 
t L. III. Weight, -f- See the 6th Note of our third Lecture, from Page 153 to 
Ann. 6, Page 159 } or more fully to fatisfy one's Curiofity, one may confult Berellfs 
Book de Mot 11 Animalium^ where he has Ihewn the particular Strength of 
the Mufcles. 

*P1. 19.F. 3. The manner of breaking the Rope as reprelented in # Fig. 3. of PL 19* 
tho' more troublefome, is alfo more effectual for breaking the Rope, than 
that which we have been defer ibing ^ for the lame Man may break a Rope 
in this Pofition, which he cannot break in the other. To underftand this 
we muft obferve, that the Man takes the Rope lb fhort, that when he 
climbs up againft the Poft, if the Eye L (thro' which the Rope paffes) 
be between his Toes, his Heels being lower at T, when his Knees are 
ftreight, the length of his Legs and Thighs T H is greater than the 
length of the Rope and Girdle from L to fo that we may confider in 
the Man and Rope the Triangle Iht drawn below the Man in the Figure; 
the Side /h, reprefenting the Length of the Rope and Diameter of the 
Girdle 5 the Bafe //, the Man's Feet $ and the longeft Side t h the extend- 
ed Limbs or the Legs and Thighs when ftreight. Now in the Rotation 
of the long Sides of this Triangle, when the Side /h comes to be horizon- 
tal at Ir (moving in the Arc hr r round the Center /, the Side / h will be 
in the Situation th (as it moves round the Center / in the Arc hh s) and 
confequently either the Rope muft ftretch from r to h y or the Point h, by 
the bending of the Knees muft be brought nearer and come to r 5 or elie 
the Rope muft break, which is what will happen, efpecially when we con- 
fider that the lower the Body (with the Limbs ftiff) comes down round 
the Heels for the Center of Motion, the greater will the Diftance xh be, 
as we may lee a little lower at r s\ lb that if the Rope did ftretch a little 
at firft, it muft break at laft, and the Man fall down upon the Feather-bed, 

or 

the Tibia. 3. The Vaftus Externus, Jpringing from the Root of the greater Rotator, and infer ted 
a little below the Patella, near the fame Place with the former. 4. The Vaftus interims, which 
arifes from the Root of the leffer Rolator, and likewife is infer ted a little below the Patella. 5 . The 

fifth is the Crureus ff ringing from the forepart of the Thigh hone^ between the two Rotators, and 

ending in the fame Place <with the former, 



A Cowje of Experimental Thilofophy. 261 



or othef fbft Body to receive him, at B. For if the Man finds that the Annotat 
A&ion of the Mufcles Extenfors of the Legs does not break the Rope y Le^ lV, 
he can in this Pofition eafily add the whole Weight of his Body with a 
Swing and a Jerk as he throws himfelf backwards/ 

The Pofture of Fig. 4. Plate 19. * (where the ftrong Man having an^Phi^.F.4, 
Anvil on his BreaU; or Belly, luffers another Man or two to ftrike with a 
Sledge Hammer and forge a Piece of Iron, or cut a Bar cold with Chiz- 
zels) tho' it ieenis lurprizing to fbme People, has nothing in it to be really 
wondered at $ for fuftaining the Anvil is the whole Matter, and the hea- 
vier the Anvil is, the lefs ar£ the Blows felt - 0 and if the Anvil was but two 
or three times heavier than the Hammer, the ftrong Man would be kilPd 
by a few Blows. This will be eafily underftood by calling to mind what 
we have faid in the feeond Le£jtyre} for the more Matter the Anvil has, 
the more Inertia and the lels liable it is to be ftruck out of its Place \ becaufe 
when it has by the Blow received the whole Momentum of thevHammer, 
its Velocity will be lb much lefs than that of the Hammer as it has more 
Matter than the Hammer. Neither are we in that Cafe to attribute to 
the Anvil a Velocity left than the Hammer in a reciprocal Proportion of 
their Maffes or Quantities of Matter ^ for that would happen only if the 
Anvil was to hang freely, in the Air (for example) by a Rope, and it 
was ftruck horizontally by the Hammer - 0 but the Refiftance of the Ribs 
which make an Arch under it, will ftill diminiih that Velocity : So that if 
the Hammer ftriking the Anvil when hung freely, could make it move an 
Inch out of its Place *, by putting a Refiftance behind it equal to the Weight 
of the Anvil it would move but half an Inch, and but a quarter of an Inch 
if that Refiftance was double, &c. Thus is the Velocity given by the 
Hammer diftributed to all the Parts of a great Stone, when it is laid upon 
the Man's Breaft to be broken } but when the Blow is given, the Man feels 
lefs of the Weight of the Stone than he did before, becaufe in the Re- 
action of the Stone,all the Parts of it round e about the Stone, rile towards the 
Blow, and if the Tenacity of the Parts of the Stone, is not ftronger than 
the Force with which it moves towards the Hammer, the Stone muft break ^ 
which it does when the Blow is ftrong and ftruck upon the Center of Gra- 
vity of the Stone. 

N.B. Ttbat the Parti of Bodies ftruck m^ve towards the Blow, is a Con- 
fequence of a Law of Nature^ which fhall be explain d in my next 
LeElure. 

I ihould be too tedious to be as particular in my Explanation of the o~ 
ther Feats of Strength as I have been in thefe above-mentioned. There- 
fore I will only lightly confider the following ones 5 efpecially, fince the 
Principles already explain'd in the Le&ures paft, and the Confederations 
juft mentioned, will enable any one eafily to difcover the Reafcn of all fuch 
Performances. 

In the 5 th Fig: of Plate i 9 . f The Man IHL (the Chairs I, L, be-tPl.ij.Rs. 
ing made fail) makes fo ftrong an Arch with his Back-bone and the Bones 
of his Legs and Thighs, as to be able not only to fuftaifr one Man, but 

three 



262 A Cmrfe of Experimental I Philofophj* 



Annotat. three or four, if they had Room to ft and j or, in their Stead, a great 
Le£h IV. Stone to be broken with one Blow. 

v^~v~\- In the 6 th and 7 th Figure of the fame Plate # a Man or two are rais'd 
*Pl.i9.F.6,jn the Dire&ion CM by the Knees of the ftrong Man IHL lying upon 
h his Back. Now we muft obferve that the five Mufcles (a) which bend the 

Legs (tho' weaker than the Extenfors, becaufe they are not to carry the 
Body in our common Motions) a& with their greateft Force at the Begir> 
ning of this Operation, as all Mufcles do when from their foil Extent they 
begin to contrail ^ and to relieve them in their A&ion as the Heels come 
forward from the Point L they flop againft the Ground and keep the Body 
M in the Place which it is rifen to : So that the Aftion of thefe Flexors is re- 
iterated, and they have time to be recruited with frelh Spirits (or whatever 
Fluid is the firft Caufe of their Inflation) and when they are fo far con- 
tracted as to a£t more weakly, the Preffure of the Weight affefts them lefs 
and lefs, the Bones fupporting more of the Weight as they become more 
perpendicular, and confequently the Mufcles have lefs occafion to a£fc. See 

* PLjy.F.i.Fig. 7. * The reft of the Performance, -viz. of letting the Man M upon 

a Table, is very eafy and obvious, the ftrong Man having now only his own 
Body to lift up, which he helps by putting his Hands round the Mans 
Feet or Hams, and in railing himfelf up, rather pufhes him off of his 
own Knees than lifts him up upon a Table plac'd at N at Arms ends, as 

f PL 19. R 7. he pretends, t 

In breaking the Rope one thing is to be obferv'd, which will much fact- 

* PL20. F. 3. litate the Performance * and that is to place the Iron Eye L, *■ thro 9 

which the Rope goes, in fiich a Situation, that a Plane going thro' its Ring 
ftall be parallel, or nearly parallel to the two Parts of the Rope 5 becaufe 
then the Rope will in a manner be jamm'd in it, and not flipping through 
it, the whole Force of the Man's Aftionwill be exerted on that part of the 
Rope which is in the Eye, which will make it break more eafily than if 
more Parts of the Rope were a&ed upon. So that the Eye, tho' made 
round and fmooth, may be laid in fome meafure to cut the Rope. And it 
is after this manner that one may break a Whip-cord, nay, a fmall 
Jack-line with ones Hand without hurting it; only by bringing one 
part of the Rope to cut the other ; that is, placing itfo round one's left 
Hand, that by a fudden Jerk, the whole Force exerted fhall a& upon one 
tPl-2o.F.n. Point of the Rope. See the nth Figure of Plate 20 t where the Cord, 
to be broken at the Point L in the left Hand, is mark'd according to its 

Courfe^ 

(a)' The five Mufcles that bend the Legs are thefe. I. The LongirTimus, or Fafcialis, arifing frcm 
the inner Knob of the Gs Ilium, and a little above the Knee ending in a Tendon ; which is inferted 
under the Knee, into the fore and inner Side of the Tibia. 2. The Gracilis fpringing from the joint- 
ing of the Os Pubis, and inferted by a ftrong Tendon a little lower than the former, in the inner Side 
of the Tibia. 3. The Seminervofus arifing from the Knob of the Ifchium, turning into a round 
Tendon under the Ham and inferted alfo into the inner Side of the Tibia towards the back-fide, running ' 
as far as its Middle, 4, The Semimembranofas proceeding from the fame. Knob., and ending by a 
broader Tendon than the third, in the hinder part of the Tibia, 5. The fifth is call" a Biceps ? 
iikewife- beginning at the lichmm^ and at laft ' inferted ' into the outer Side of the- upper Appendix'^ 
the Fibula. 



ACourfeof Experimental Philo/opby, a$g 

Courfe, by the Leters RTSLMNOPQ., folding once about die right 5 4$tnotat 

Hand, then going under the Thumb into the middle of the left Hand,Le£h IV S 

where crofting under another Part it is brought back under the Thumb a- i*/~Y m \J 

gain to M, then round the back of the Hand to N, fo thro' the Loop at 

L to O, and three times round the little Finger at P and Q j which laft 

is only that the Loop N O may not give way. Before the Hands are 

jerk'd from one another, the left Hand muft be fliut, but the Thumb 

muft be held loofe, left preffing againft the Fore-finger it Ihould hinder 

the Part T L of the Rope from carrying the Force fully to the Point L y 

but the little Finger and that next to it muft be held hard, to keep the 

Loop N O firm in its Place. 

The making ule of the Mufcles that extend the Legs for lifting great 
Weights is no uncommon Pra&ice among fome of our working Men, tho 5 
it is not obferv'd, becaule it is done without an apparatus. We fee Hack- 
ney Coach-men often get out of their Boxes and with their Rumps eafily 
lift up the Coach behind to make way for one another, or to avoid ibme 
great Rub, or fome Hole, or any other Inconveniency 5 and this they 
do with fo much eafe, that if they have four Perfbns in the Coach, and 
three or four Trunks behind, they never think it worth while to defire 
any Perfon to get out, or to take off any of the Weight. The Coal- 
Porters at the Cuftom-houfe Key (commonly calPd Fellow/hip Porters} car- 
ry one hundred and three quarters Weight of Coals, running all the way, 
tho' at every Turn they go up two Ladders, and often the length of St. 
Dunftatis Hill, which is a Street pretty fteep and ill pav'd, and perhaps 
climb up a Stair-cafe or two before they fhoot their Coals : and this moft 
of them will do above fixty times a Day. But their manner of doing it, 
is to ftoop fo as to let the Sack bear chiefly on their Rumps, holding one 
Hand behind them to keep together the Mouth of the Sack, that they 
may with more Expedition ihoot out their Coals, whilft their other Hand 
fecures the Sack from flipping down from above ^ and this Pofture very much 
eafes the Aftion of the Mufcles of the Loyns, the Extenfors of the Legs 
being then chiefly concerned. 

Since I began to write this, I have been credibly informed that the Porters 
in -Turkey carry feven or eight, nay fometimes nine hundred Weight upon 
the lower end of their Back, or rather their Rump, only refting on a Stick 
before them, whilft they receive their Loads, to fupport their Body and 
fave the Mufcles of their Loyns 5 but we may eafily guefs that other Per- 
fons muft be very careful in putting on and taking off the Burthen. 

I believe the Strength of the tfeftudo made by the Roman Soldiers when 
they ftood clofe together with their Shields over their Heads, muft be ow- 
ing to fome fuch fort of Pofture of the Body : otherwife they could never 
have been able to bear the Weight of Chariots driving over them, as 
fome Hiftorians have inform'd us. In that Cafe evei;y Man, except thofe 
of the firft Row, (a) covered the Man who ftood before with his Shield 

at 

(a) Thofe of the firft Row held their Shields inclined before them as they ftoofd. Sometimes the 
firft Row kneeled, and the fecond Row bore on the Shoulders of the firft as they ftoof d,, and cover* i' 
them with their Shields 1 &c. 



%66 A Courfe of Experimental } Phihfophy, 

Annotat. at the fame time bearing upon his Rump that flood before him : and when 
Led. JV. they flood againft any Shock, their Mufcles had no other Labour but to 

^*~ss~^ keep their Knees ftiff* the bony Arch already defcrib'd f being fufficient 
t PI. 20. V.6. to fupport a much greater Weight. 

^ There are feveral Cafes, wherein it would be of lingular ufe to apply the 
Force of one or more Men, by means of the Girdle and Hook and Chain,, 
in the manner abovementioned y as for example, when the Refiftance is 
very great, but the Bodies that refift are to be remov'd but a little way: if 
we lift very heavy Goods a fmall Height to remove any thing from under 
them: if we would draw a Bolt or Staple, and find we can't do it even with 
an Iron Crow, the Hand pulling it upwards at the End, then the Hook of 
the Girdle being applied at the End of the Crow, the Force exerted by 
ftretching the Legs would be tenfold of what the Hands were able to do 
without more help at the fame Place. * 
There may alio be many Occafions on Board a Ship. I'll inftance but 
* Pl.2uE1.one. Let FG * be the Tackle for raifing or lowering the Main-top-maft, 
part of which is reprefented by mi, m the Block G is fix'd below, 
and as the Block F comes down it pulls along with it the top Ropes F B C 
m i running over the BlockB (fix'd at A) and round the Block C in the 
Heel of the Top-maft, lb as to draw up the lower End m i of the laid 
Main-top-maft, which when hoifted up to its due Height, is made faft by 
the Iron Pin or Fidd I which is thruft thro' it, and then its own Weight 
and the Hole D of the Cap will keep it in its Place. We'll fuppofe that 
the Force requir'd thus to raife the Maft muft be that of fix Men pulling 
upon Deck at the fall of the Tackle, that is, at the running Rope F G K at 
K on the other fide of the Main-maft L 1. Now in order to let down this 
Maft on the Hidden, as in cafe of hard Weather it is neceffary, the fame 
Tackle and Power muft be made ule of, tho' it be but to lift it a very 
little Way, that a Man may be able to get out the Fidd I before the faid 
Maft can be let down and flip to N on the fide of the Main-maft, I fay 
that if the Hands are lb employ'd otherwile, that inftead of fix Men there 
be only one Man at the Rope K} if he has a ftrong Girdle to which he 
fattens it (or makes a Bow in the Rope it felf to fix it round the lower 
part of his Back, &c.) he may exert much more Force in the Direction 
G K than the fix Men in the common way of pulling : and if he draws to 
him (fitting on the Ground and pulhing his Feet againft the firft firm Ob- 
ftacle that he finds, as againft O P) only two Inches of the Rope K G 
he will raife up the Main-top-maft the third part of an Inch, which will 
be fufficient for the Iron or Fidd I to be drawn out. 

N. B. If more Force JhouU be requir'd for this Operation, as in large 
Ships, feveral Men at once might make ufe of Ropes about their Mid- 
dles inftead of Girdles, and faft en them all to different parts of the Fall of 
the Tackle; and for fix'd Points they might Jet their Feet againft the 
wooden Steps of a Stern Ladder taken down and lying on the Deck 
faften'd at one end to one of the Ring Bolts : for tho' in this cafe etch 
Man could not apply fo much Force as the fingU Man before fuppos'd, 

becaufb 



A Courfe of Experimental Philofophy. 



becaufe as they all mufl fit a little on one fide of the Rope G K, their Annotat.* 
Pull will he fomething oblique - ? yet fiv£ Men in this cafe, will very Left. IV 
eafly do the Work of fifteen. 

8. D?age 243.— — Y*he whole Force whereby a Man draws r &c. ■ I have 
given a Tranjlation in my Notes, &c] 

To illuftrate and confirm what I have fa id in the Lefture, 1 fhall here 
give part of Monfi De la Hire's Memoire given in to the Royal Academy of 
Sciences, in the fear 1699, entitled, jin Examination of the Force of Men 
to move Weights, whether by lifting, carrying, or drawing ; confided d as well 
abfolutely as when compar d with that of other Animals which carry and draw, as 
Horfes, &c. In which all his Reafbning is juft, tho' lome of his Data be- 
ing wrong, lead us alfo to a wrong Conclufionj but I fhall let all right by 
my Obfervations upon it. 

" I fuppole firft that a Man of a middle Stature who is pretty ftrong, 
" weighs 140 % of our Weight. (*) I confider firft, that fuch a Man as 
cc I have fuppos'd, having both Knees on the Ground, can rife bearing only 
" on his Toes, ftill keeping his Knees together } and as this Action is per- 
<c form'd by means of the Mufcles of the Legs and Thighs, it is evident 
€C by the Suppofition I made of his Weight, that the Mufcles of the Legs 
€C and Thighs have a fufficient Force to raife 140 lb. 00 

u But a Man bending a little in the Hams can raife himlelf up though 
<c loaded with a Weight of 150 lb, together with the Weight of his Bo- 
cc dy, which he raifes at the lame time:, (b) lb that the Force of the 
" Mufcles of the Legs and Thighs can raile a Weight of 290 lb, that is 
" 150 lb the Burthen carried, and 140 ft> the Weight of the Body, when 
<c the Rile is but 2 or 3 Inches. 

" Such a Man, as we have fuppos'd, and fhall all along fuppofe him, can 
cc alfo lift from the Ground a Weight of ioafo plac'd between his Legs, 
" taking hold of it with his Hands as with two Hooks, and raifing him- 
" lelf up. (c) Whence it follows that the Mufcles of the Loyns alone 
u have Force enough to raife 1 70 ife, namely, the 100 lb of th^ Weight, 
" and 70 lb half the Weight of the Man 5 becaufe he is to raife not only 
" the 100 lb Weight, but alfo the whole upper part of his Body above the 
a middle, becaufe we have fuppos'd him to ftoop to take up the Weight. 

" As for the ftrength of the Arms for drawing or lifting a Weight, one 
" may fuppofe it of 160 lb, which depends upon the Mufcles of theShoul- 
cc ders and Arms. For if a Man with both Hands takes hold of fome 
" fix'd Body plac'd over his Head, he may eafily enough, by the ftrength 
a of his Arms alone, draw up his Body, and even 20 lb more, juft as if 
cc he was burthen'd with a Weight of 20 lb* It is eafy to make the iixperi- 
" ment } for if a Weight of 160 lb be faften'd to a Rope and thrown o- 
c< ver a Pulley, and a Man who weighs only 140 Ifo pulls at the other end 

Mm « of 



(a) The French lb w betwixt one wth and one nth f art greater than our Pound Averdupoids. 



268 A Courfe of Experimental Phihfophy. 



Annotat. u of the Rope, it is plain that he will never be able to raife the 160 ife 
Le£t. TV." Weight} the utmoft he can do being only to hang with all the Weight 
u^YV cc of his Body by the Rope*, for the Weight at the other end being great- 
a er than the Weight of the Man, will keep him futpended j the Pulley 
iC being only a continued Balance with equal Arms : but if the Man has 
a faften'd to him a Weight of 20 fo, then he will make an ^Equilibrium 
a with the Weight on the other Side > and if ever To little be added to the 
" 20 ib Weight he will raife the oppofite Weight, the Mufcles of his 
u Shoulders and Arms being of fufficient Force to fuftain the whole ag- 
a gregate Weight. 

a Tho' the Mufcles of each part of the Body can exert great Forces 
a to raife Weights, the Force of a Man is not to be reckoned as the Sum 
u of the different Forces of all his Mufcles taken together, even tho' the 
• <c Spirits which fwell the Mufcles, and by fhortening them draw the Ten- 
" dons at their Ends coif d as eafily be diftributed to all the Parts as to any one 
" particular Part, becaufe each Part commonly ferves to fiipport that which is 
" immediately next to it. As for Example; the Mufcles of the Arms and 
a Shoulders by their Contraction can lift a Weight of 160 ft^ but if the 
" Body be inclined, the Arms will not be able to fnftain that Weight, unlefs 
<c the Mufcles of the Loyns are at the fame time Strong enough to fuftain the 
" upper part of the Body, together with the Weight which it is loaded 
<c with-, and if the Hams were alfo bent, then the Mufcles of the Legs 
" and Thighs muft ftill exert a greater Strength, becaufe they muft fuftain 
<c the Weight of Jdoft, and alfo at the fame time the whole Weight of 
€C the Body, Whence it happens, that in this Difpofition of the whole 
cc Body, the Force is diftributed by the Diftribution of the Spirits into 
all the Parts ; for which reafbn a Man will not be able to raife 160 jfe: 
a from the Ground. 

<c Not but there are Men, whole Spirits flow fb abundantly and fb fwift- 
cc ly into their Mufcles, that they exert three or four times more Strength 
c< than others do;, and this leems to me to be the natural reafbn of the 
a furprizing Strength that we fee in fome Men who carry and raife Weights 
cc which two or three ordinary Men can hardly fuftain, tho' thefe Men be 
a fometimes but of a moderate Stature, and rather appear weak than 
cc ftrong. There was a Man in this Country a little while ago, who woif d 
" carry a very large Anvil, and of whom were reported feveral wonderful 
a Feats of Strength; but I law another at Venice^ who was but a Lad, 
" and did not feem able to carry above 40 or 50 ife with all poftible Ad- 
" vantages: Yet this young Fellow {landing upon a Table, rais'd from the 
u Earth and fuftain'd off of the Ground an Afs, by means ofa broad Girt, 
cc which going under the Creature's Belly, was hung on to two Hooks that 
" were faften'd to a Plat of fmall Cords, coming down in Treffes from the 
<c Hair on each fide the Lad's Head, which were in no great Quantity 5, 
€c and all this great Force depended only upon the Mufcles of the Should- 
" ers and thofe of the Loyns (d)) for he ftoop'd at firft whilft the Hooks 
a were faften'd to the Girt, and then rais'd himfelf and lifted up the Afs 

€C from 



A Omrfe of Experimental Philofophy. 269 



€: from the Ground, bearing with his Hands upon his Knees. He raised Annbtat. 
« alfo in the lame manner other Weights that feem'd heavier, and us'd to Le£t. IV* 
" lay he did it with more eafe, becaufe the Afs kick'd and ftruggled when |/Y\J 
£C firfl lifted off of the Ground, (e) 

" Now to examine the Force of a Man to carry a Burthen upon his Shoul- 
£C ders; I lay that Weight may be of 150.it}, and a Man may walk with 
" that Load eafily enough upon an horizontal Plane, provided he does not 
" take great Steps j but he can by no means go up a Mountain or a Stair- 
cc cafe with the lame Weight. For the A£fcion of walking, when we bear a 
cc Burthen, snuft be confidcr'd as the circular Motion of C, the common Gen- PL 20. F. 
cc ter of Gravity of the Body and the Weight together about the Foot F, ia« 
" that advances as the Center of the Arc of Motion, the Effort of the 
iC Mufcles of the other Leg which aft againft the fix'd Point D, ferving 
"only to drive the Center of Gravity forward 5 and if the Arc CE, 
" which that Center defcribes, be fmall, the Effort of the hind Leg need 
<c not be great to make the Center defcribe it 5 becaufe then it puihes up 
cc the Weight of the Body, and the Burthen only the Height of A B the 
" vers'd Sine of half the Arc, which is inconfiderable in this Cafe in re- 
cc IpeO: to the whole Arc, which is the length that the Burthen advances. 

cc So that a Man carrying a Burthen, can walk lb much the eafier as his Steps 
" are fhorter, becaufe the vers'd Sine will be fo much the lels \ for if he fhoq'd 
cc take Jarge Steps, the hind Leg muft puih up the Body and Burthen the 
" Height of the vers'd Sine of fo much a greater Arc as the Steps are 
" greater J that is, the vers'd Sine of the Arc which meafures half the Di* 
" ftance that the Burthen advances forward. 

" It is alio plain, that a Man thus loaded can by no means go up a Stair- 
cc cafe, or a very fteep Hill with that Burthen 5 becaufe according to what 
a we have already explained, the A&ion of the Mufcles of the Legs being 
u only able to raife a Weight of 150 ife to the Height of two or three Inches, 
cc he wou'd not be able to raife it five Inches, which is the Height of 
u common Stairs or Steps, (/) nor go up a Mountain, unlefs he took luch 
u lhort Steps as to rife only two or three Inches perpendicularly every time. 

a What remains now is to confider the Force of a Man for drawing or 
cc thrufting horizontally, (g) But to make this the more clear and intelligi- 
" ble, I ftall confider that Force as apply'd to the Handle of a Roller or 
<c Windlafs whole Axel is horizontal, on which Axel the Rope which fuf- 
cc tains the Weight winds up, fuppofing the Diftance from the Center of the 
cc Roller to the Elbow of the Handle to be equal to the half Diameter 
€C of the Roller, that the Force applied may be eftimated without #ny 
<c Augmentation on account of the Machine : neither do I confider here 
cc the Friftion of the Pivot or Difficulty of folding the Rope. 

u Fir ft then, it is plain, that if the Elbow of the Handle be in an hori- 
cc zontal Situation, and about the Height of a Man's Knees, a Man that 
£C lifts it by drawing up, may exert a Force capable of railing 150 % 
u hanging at the end of the Rope if he takes all pofltble Advantages, ac- 
u cording to what I have already explain'd. But if he is to deprefs the 

Mm 2 Handle 



270 A Courfe of Experimental Philofophy. 

Annotat. " Handle his Strength for that purpofe cannot be more than equal to i to «s 
Led- IV. " which (as has been fuppos'd) is the Weight of his Body j for he can 

" ~ 1 \7r .°u "° T r , e W f igI ^ than that > exce l u he vvas load ed with fome 
Weight, and then the fcffefl might be fo much greater. 

" .Secondly, If the Elbow of the Handle be plac'd vertically, and it be at 
the fame Height as a Man's Shoulders, it is certain that a Man can ex- 
t ?u n °u F ?5 Ce t0 Caufe k t0 turn ' ^ P ulhin S or drawing with his Hands. 
*™ i, « • T?.' CCt L be ? S / e . C t0 § e i her the Bod y ^ upright as reprefented 
*H. 2 o.F.i> in *Ftg. 13. by the Line AP, the Line A M reprelenting the line of 

the Arms being horizontal, and making a right Angle with AP } be- 
caufe in that Portion, neither the Force of the whole Body, nor of any 
" part of it, nor its Weight, can exert any Force for drawing or pufliing- 
which is known by Mechanicks > for I look upon the Breadth taken up 
" by the Feet but as a Point at P. But if the Handle be higher or lower 
" than the Level of the Shoulders, then the Line A M, which goes from 
the Shoulders to the Hands, and the Line A P going from the Shoulders 
" to the Feet, will make an obtule or an acute Angle, and then a Man 
may exert fome Force for drawing or pulhing the Handle ; but that 
t-orce depends only upon the Weight of the Body, as may be eafily per- 
ceivd and demonftratedj and that Weight or Force muft be confider'd 
" as colleaed in one Point, which is the Center of Gravity of the Body, 
" and about the Height of the Navel: 1 fay, we muft have regard only 
" to the Weight of the Body, in order to determine the ^Equilibrium 5 for 
*« the Aaion of the Mufcles of the Legs and Thighs ferves only to pre- 
" ferve that ^Equilibrium as we walk. 
* PI. 21. F.i. « Let the Handle in Fig. u * be plac'd at D the fame height as the 
" Shoulders A, and the Center of Gravity of the Body be at C, the Body 
" being very much inclin'd towards the Handle } but the End of the Feet 
" muft be at P. Firjl, We muft confider that Point P as the Fulcrum or 
" Center of Motion of a Leaver or ftrait Rod PCH, which going thro' 
" C the Center of Gravity of the whole Body meets the Line of the 
" Arms M A at the Point H. Secondly, We muft confider the Point C of 
" theLeaver loaded with the whole Weight of the Body equal to 140 % 
" which Weight endeavours to defcend perpendicularly according to its na- 
" tural Diredion, the end H of the Leaver being fuftain'd in thehorizon- 
" tal Direffion M A H ; whence it will be eafy to determine by mechani- 
" cal Principles, what Effect the Weight of the Body at C, afting in its 
" natural Direaion, cm have on the Handle according to the horizontal 
" Direaion HD. 

" For, firft, let us fuppofe PH to be divided into 240 Parts, of which 
" PC contains 80. Now fmce the Weight of the whole Body aaing at 
" C is but 140 |b, when apply'd at H it will aft but with the Force of §0 



...... ^„ i-v^vu-icuiai mn. xi Luctctoic irom cne center or Mo- 

" P the Sine PF be drawn perpendicular to M A F, the Weight 



11 



A Courje of Experimental Philofophy. 271 



a of 80 ft at H afting in its natural Direction: will be to the A&ion of Annotate 
" the fame Weight upon the Handle according to the horizontal Direfti- Le£L IV* 
« on M A H ; : in the Ratio of P F : to H F. And this does very much cA^V 
" diminifh the Affion of the 80 ft in a moderate Inclination of the Body 
" A C B. And if we fuppofe for Example, that the Line PC H makes an 
<c Angle P H F of 70 Degrees with the Line M A F, the Line of the Bo- 
" dy A G B will then be inclined to the Horizon in an Angle of more than 
" 60 Degrees, which is the greateft Inclination of Body with which a 
cc Man can walk} then 

cc The Sine of 70 Degrees, which is P F : 
" Will be to the Sine of its Complement, which is H F ' : 

<c As q : 

" To 1 , nearly 

" And confequently the Aftion of the 80 ib fuppos'd to aft at H accord- 
cc ing to the natural Direction, will be to the Affion exerted in the hori« 
<c zontal Direction, but as 80 to its third, which is fomething lefs than 

" *7 ft- 

" Thofe who have not made the Experiment of puftung horizontally with 
" the Arms, or drawing a Rope horizontally as a Man walks with the Bo- 
u dy inclined forward, whether the Rope be faften ? d towards the Should- 
€c ers or towards the middle of the Body (for the Effeft will not differ pro- 
"vided the Inclination of the Body is the fame-, becaufe the Sine of In- 
u clination and its Compliment are always in the Fame Ratio) can hardly 
<c be perfuaded that the whole Force of a Man is reducd to fo-little in 
cc pulling horizontally as not to exceed 27ft. 

" Not but that a Man may lean or incline; his Body fo as to fuftkin a 
" much greater Weight than 27 ft; for if the Line PH Ihould make an 
" Angle of 45 Degrees with HF, it is certain that the Weight of the 
" Body would fnftain 70 ft, but as he muft then have his Body in the 
" Pofition of the Line A B much more inclin'd to the Horizon than 45 
" Degrees, he would be fo far from being able to walk, that he would not 
" be able to ftand in fuch a Pofture. 

" The fame Demonftration may alfo ferve to foe w that a Man has much 
" more Force to draw if he goes backwards than in going forwards. For 
" in fuch a Situation of the Body, the Line PCH, * Fig. 2. which goes * PI.21.F.2. 
" from the Feet at P thro 5 the Center of Gravity C, and on which the 
" Encreafe of Force depends, will always be much more inclin'd to the Bo- 
c< rizon than the Line of the Body AC B, quite contrary to what it was 
" in the former Pofition. But then this way of drawing cannot be put in 
<c pra&ice, except for pulling a Rope, when a Man continues in the lame 
<c Place -, otherwife we Ihould naturally come into that Pofture y for Nature 
« and Experience have taught us to take all poffible Advantages in common 
<c Operations. 

" For the fame Rea Ton Watermen and thofe that row at Sea always pull 
" their Cars backward $ for that way they can exert more Force than in 
« pu filing forwards iike the Gondolier's at Venice 7 who work in that manner, 

x " tor 



2?2 A Courfe of Experimental Phihfophy. 

Annbtat, u for no other Reafon than to fee well before them, which is more neceffa* 
Left. IV. " H to Aem than exerting a great Force, by reafon of the many fhort 
v^"v~ ^ u Turns they mult make in the Canals, and the Care they miift take to a- 

" void one another," 

What remains is to compare the Force of Men with that of Horfes 

for drawing, &c. but having confider'd that in myLefture, I need not give 

the Tranflation of the reft of Monf de la Hires Paper-, only proceed to 

apake my Obfervations upon it. 

(a) The Mufcks of the Legs and Thighs are much fir anger than M. De la 
Hire fappofes? as appears by what has been [aid concerning the Feats of 
Strength \ and the ASlion of rifing backwards from ones Knees is very fhort 
of the utmoft that a Man can do in that Pofiure ? for a Man may carry fome 
confider able Weight and yet rife from his Knees? tho* the Arc defcriVd by the 
Center of Gravity be then an Arc of a good many Degrees. 

(b) is ufual in London for Men to raife themfelves up with? and carry 
2)0 %? which is almofi as much more as M. De la Hire has fuppofd - 0 there* 
fore all the Confluences drawn from this Suppofition mufi fall fhort. 

(c) Working Men generally lift i 50 % with their Hands? and fome 200 ft> % 
but here the Excefs of the Force of the Mufcles of the Loyns is not fo much 
greater than M. De la Hire's Suppofition? as the Excefs of the Force of the 
Mufcles of the Legs. 

(d) What he attributes here to the Mufcles of the Loyns was really per* 
formed by the Extenfors of the Ljegs -? for the young Man's ftooping with his 
Hands upon his Knees was not with his Body forwards and his Knees fiiff? but 
his Body upright and his Knees bent? fo as to bring ¥be two Cords with which he 
lifted to be in the fame Plane with his Ankles and the Heads of his Thigh- 
Bones, by which means the Line of Diredlion of the Man and the whole 
Weight came between the ftrongefi part of his two Feet? which are the Sup- 
ports : then as he extended his Legs he raised himfelf without changing the 
Line of Direction. That this mufi have been the manner I am pretty well af- 
fufd of? by not only obferving thofe that perform fuch Feats? but having often 
trtfd it myfelfi As for the Mufcles of the Loyns? they are incapable of that 
Strain? being. above fix times weaker than the Extenfors of the Legs? at leafi 
I found them fo in myfelf. 

About the Tear 17 id, having the Honour of fie wing a great many Experi- 
ments to his late Majefty King George the Firft, his Majefty was defe- 
rous to know whether there was any Fallacy in thofe Feats of Strength that had 
been Jhewn half a Tear before by a Man? who feern^d by his Make to be no 
fironger than other Men : upon this I had a Frame of Wood made to fiand 
* PI.20.F.2.*"* Cf uc h as is reprefentedby the 2d * Fig. of Plate 20.) and with a Girdle and 
Chain lifted an Iron Cylinder made ufe of to roll the Garden? fufiaining it eafily 
when once it was up. Some Noblemen and Gentlemen who were pre fent? trtfd 
the Experiment afterwards? and lifted the Roller , fome with more Eafe? and 
fome with more Difficulty than I had done. This Roller weighed 1900 %? as 
the Gardener told us. Afterwards I try* d to lift 300 % with my Hands (viz, 

two 



A Courfe of Experimental Phikfophy. 273 

two Pails with i ~o ib of Quickfilver in each) which 1 did indeed raife from Annotate 
the Ground^ but flrairfd my Back fo as to feel it three or four Days - 0 which Le£t. IV* 
Jhews that) in the fame Perfon, the Mufcles of the Loyns (which exerted their U^Y^SJL 
Force in this lafl Experiment) are more than fix times weaker than the Ex- 
tenfors of the Legs \ for I felt no Inconveniency from raifing the Iron Roller. 

(e) The Reafon why the Afs kicking and moving made ^hi's Weight more in- 
convenient than an heavier Burthen^ was, that by fuch a Motion the Line 
of Direction vacillated^ and as it went forwards and backwards y the Mufcles 
of the Loyns were forced to aft to bring it into its Place again. 

(f) fhat JVL De la Hire has taken the Strength of the Mufcles that ex- 
tend the Leg and ftretch the Foot 7 too little) appears from the Practice of all 
thofe. that carry Grain in Sacks and Meal) who eafily go up Stairs with 200, 
and often above 250 ib Weight; and the Men who carry Coals from Carts in- 
to Houfe^go up Stairs with 250 ^ Weight, they can't indeed go down Stairs 
with fo great a Weight as they can go up. 

(g) All that follows in this Differ tation concerning a Man's pujhing or draw- 
in? may be depended upon\ becaufe it is mathematically deduced from the 
Weight fuppos'd) and cannot but be true in a Man weighing 140 

9. [Page 2^.— -there muft be a fufficient Velocity given y &c] If there 
fkonld be no greater Velocity given to the Hand which is to turn the Winch, 
than I have fuppos'd, there could not be Motion enough communicated from 
the advantageous to the difadvantageous part of the Revolution, as would 
enable a Man to raife 30 ib with the fame Velocity as the Hand mov'd: 
therefore we muft fo contrive Matters as to encreafe the Velocity of the 
Hand moving, at leaft one fixth party but then we muft lay only 25 ib upon 
the Hand moving fo much the fwifter, which yet will perform as much Work 
in a Day as if the other way had been practicable. Nay, in a great many 
Cafes it will not be amifs to give the Hand one third more Velocity, and load 
it but with 20 ib, efpecially if a Fly be made ufe of 5 and the bigger the 
Circle is which the Fly describes, the better will the Force be diftributed. 
This Work thus perform'd may be continued ten Hours a Day, and very 
little fatigue the Labourer. 

10. [Page 24^ — Daily Labour of the London Porter s 7 &c] At the 
Cufiom-houfe Key, and at feveral Wharfs one may obferve what great Loads 
are carry'd by Porters employ'd to carry Goods to and from the Veflelson 
the Water: Such indeed are the Loads which fome carry, that an Horfe 
would foon be kiil'd by carrying the fame Weight. They that work for the 
Cheefemongers at fo much per ton) generally carry 300 Weight of Cheefe at 
every Turn, and work all Day long. 

11. [page 247.-— theHorfes ftrong 7 &'c.] If too great a Load belaid 
upon an Horfe's Back, there is danger of breaking it ; which is the Reafon 
that People do not generally lay on vety great Loads. The Felt-mongers 
and Skinners, are faid to load their Horfes more than any other People 3 but 



274 A Courfe of Experimental Phihfophy. 

Annotat. they lay federal Skins and Hides over the Horfes Shoulders and Hips, that 
Left. VL the Back may not be too much ftrain'd: I am informed that they put on 
i/YV fometimes 4 or 500 Weight; but then the Horfes go extremely flow. 

The moft that can be done with an Horfe is to make him draw : and thole 
Horfes that do moft Work are fuch as draw great Loads in Carts on ve- 
ry high Wheels (the Horfes themfelves being very tail) up St. Dunftan's 
Hill in the Eaft 9 where a Carter does fometimes lay on 2000 lb Weight, 
and makes one Horfe draw it up the Hill; but at every difficult Place, the 
Manfets his Shoulder to the Cart in fuch a manner, as confiderably to help 
the Horfe, who would be unable to draw up the Load without that Help : 
and fb fenfible is the Horfe of it, that he does not exert his whole Strength, 
till he finds that his Matter helps him. 

I promised in the 15 th Note to Lett. III. to give an Account of Mr. AU 
Jenh Carriages at Bath,, and having juft receiv'd the Account from a Friend 
well skilPd in Mechanicks and drawing, who took the Meafures and Draughts 
upon the Place, think proper to communicate it here, as having confider'd 
the Nature of Carriages in this Lecture. 

A Description of the Carriages made ufe of hy Ralph Allen, Efqy to 
carry Stone from his Quarries, fituated on the top of a Hill, to the fVa- 
ter-fide of the River Avon, near the City of Bath. By Charles de 
Labelye. 

Thefe Quarries are at the Diftance of a Mile and an half from the River, 
and about 500 Feet above the Level of its Surface, which makes a Slope fo 
ftcep, that thefmall Price the Stone is fold at, would hardly defray the 
Charges of bringing it down without feme proper Contrivance, fuch as the 
folio wing,which is a great Improvement on lome Carriages and Waggon-ways 
made ufe of at the Coal Mines near New-Gaftle. 

*P1.2i.F.4. i. Fig. 4. Plate 21. # reprefents this Carriage in Perfpe&ive, as feen 
from a Diftance of 12 Feet from the left of the fore Wheels, the Height 
of the Eye being about 6 Feet. The Geometrical Plan was laid down from 
a Scale of 20 to an Inch} that is, every 20th of an Inch, anfvers to one 
Inch in the Machine. 

*Pl.2i. F.5. 2. 5. * reprefents the Elevation of one of the Sides of this 
Carriage, when both the Fore- wheei and Hind- wheel of that Side are lock'd, 
from a Scale of 20 to an Inch. 

tP1.2i.F.d. 3d. Fig. the 6th. f reprefents the Elevation of the hind part of the 
Carriages, with all the Iron- work employed in the locking of the Wheels, 
and it ftiews alfo the Profit of the Wheels, and i^xel-tree, together with 
the Sections of the Side-pJanks and of the Frame on which it moves, from 
a Scale of 10 to an Inch. 

4. From the Confideration of thefe three Figures, it will appear, that 
this Carriage confifts of a ftrong Floor of (Oaken) Planks, three and a 

half 



A Courfeof Experimental Philojophy. t 

Italf Feet wide, and about 13 Feet long, ftrengthen'd above by feveral Annotate 
Ribs to defend it from the Stones that lye upon it, and fix'd upon four Le'&.lV. 
Beams of the fame Wood, about four Inches fquare and 14 Feet long, s^s^^j 

.5. At fix Inches from the Ends are fix'd the fore-fide and back-fide 
ftrongly faflen'd to the Beams, and to the Floor, by feveral Screws and Nuts, 
See Fig. 4 and 6. -f fP1.2i.F.4, 

6. To thefe two Ends, when Occafion requires, , may be faflen'd two and 69 
Sides made of Planks 13 Feet long, which fit into the Side of the outward 
Beams by means of Hooks and Rings, and are kept up by means of Latches 

to be feen in Fig. 4, 5, <5. Thefe Sides are alfb further ftrengthen'd by a f Pi. si. P. 4, 
Chain going acrofs in the middle of the Carriage. 5, and 6, 

7. At right Angles under thefe Beams, at a proper Diftance (fee Fig. 
5.) are faflen'd twoftrong Timbers, by means of large Screws and Nuts. 

8. In thefe Timbers well ftrengthen'd and plated with Iron, where the 
greateft Strefs lies, are placed two femicylindrical Pieces of Brafs at each Fnd^ 
to ferve as a Collar for the Axel-trees of the Wheels, which being well 
greafed, turn with very little Fri&ion. 

9. There is likewife under thefe four Beams (already mentioned) another 
piece of Timber of about 6 Inches by 4 well faflen'd to it, at right Angles, 
and at fuch a Diftance, as is feen in Fig. 5. 

This Piece ferves as a fix'd Point to place a Leaver, which locks (or 
keeps from turning) the Hind-wheel, by prefling upon it. 

10. The Axel-tree is about three Inches Diameter. See -f Plate 22. Fig. f pj.aa.F. 1; 
1. One of its Ends is fquare, the other round, and on thefe two Ends, the 
Wheels are plac'd in an alternate Pofition ; that is, the right-handed Fore- 
wheel is on a Square, and the left on a round part of the Axel-tree, whilft 

the right-handed Hind-wheel is on a round End, and the left on a fquare 
End of the Axel- tree thereby any one of the Wheels may be lock'd fepa- 
rately for when the Wheel placed on the round End is lock'd, the other, 
together with the Axel-tree, revolts within it, and when the Wheel which 
is faflen'd on the fquare is lock'd ; the other revolves notwithftanding as 
ufiial upon the Axel-tree, which is then immoveable. 

ji. Thefe Wheels are made of caft Iron about 20 Inches Diameter, and 
have a Flanch 6 Inches broad next to the Carriage which hinders them from 
running off from the Oaken Frame on which they move. Their Plan and 
Profil are feen in Fig. f of Plate 21, and Fig. 1. of Plate 22. and their j pi, 2 i.F. | 
Seftions either thro' their Spokes (or Radii) or between any two of them, as&Ph22F.i, 
-J- Fig. 3d and 4 th of Plate 27. . tPUs/F.3 

i2th* The manner of locking and unlocking the of the Wheels is as fol- and 4o 
lows : When either of the Hind-wheels is to be lock'd, a ftrong Leaver 
(which they call the Jigg Pole) is placed on that End of the Timber (de- 
fcribed in Paragraph 9.) next to the Wheel to be lock'd, and after it is 
paired thro' the Iron Loop to fecure it the better, a Chain coming from 
the Roller to be feen in ^ Fig. 5 and Fig. 1 of Plate 22. is clapt over the-j-pi. 21. F.5 
Extremity, and by means of a ihort iron Bar, and the Rocket and Click, &P.22.F.1. 
feen in Fig. 5 and 6 Plate 2?, * one of the Drivers or Perfbns that attend *pi. 22 .F. 5, 
the Carriage in a very little time flops the Wheel either partly or intirely.and 6. 

Nn To 



276 A Courfe of Experimental Philofophy, 

Annotat. To unlock which, 'tis only lifting up the End of the Click or Catch made 
Le£t. IV l° n S on purpofe, for then the Leaver prefling no longer, the Chain is flao 
u^V^W*ken'd, taken off, and the Jigg Pole laid in the Cart, till another Occafion 
ferves. They have two Jigg Poles, one for each Hind-wheel. 

1 3 . The Fore- wheels are lock'd, by means of a thick fquare iron Bolt, 
tPl.sti.F. 5. feen in Fig. 5 of Plate 21. *[ coming out in the Direction of the Axel-tree, 
between the Spokes or Radii of the Fore-wheels : thefe Bolts, are pro- 
truded forwards to lock the Wheels, and drawn back to unlock them 
feparately, by means of a Contrivance, part of which is feen in "Fig. y« 
t Pi. 2,1. F. 5 of PL a. and ifl: of PL 22. f Towards the middle of the back-fide are 
PI. 2i. F. 1. two iron Rods, (fee one in Fig. 6. PL .'22.*) turning feparately on the fquare 
*P1 22.B..6. 0 ^ an ^ xe ] a When either of thefe is brought by the Hand from a verti- 
cal Pofition, in which they are drawn, tp an horizontal one, the iron Rbd 9 
of which it takes hold by its lower End, is puflied forward four or five 
PI 23. F. i. Inches, and by means of the Contrivance in ."J- Fig. i 7 2, 3, 4, of PL 23. 
4. fhoots the fquare Bolt between the Spokes or Radii. 

When the Wheel muft be unlocked, this Bolt is drawn back into its for- 
mer Pofition, by bringing the iron Rod into its former vertical Situation, as 
tPl.22. F. 1. in Fig. 1. of PI. 22. f As thefe Carriages are loaded with a confiderable 
(often with upwards of four Tons) Weight of Stone, when they come 
down the Hill, all the Contrivances explained above would be ufelefs, and 
that great Weight would fink the Carriage too deep into the Ground, with- 
out pieces of Oak laid all along the Way which thefe Carriages then pafs 0- 
*P1.2i.F.4, ver - Thefe are fufficiently feen in Fig. 4, 5, of PL 21. * and fig. i.of PL 22. 
5/andP1.22. Altho' thefe Carriages are very heavy even when empty, yet by means 
F 0 !• of the Frame on which they move and the little Friftion the Axel-trees 
feel revolving in the brafs Collars,two Horfes not only draw up them the Hill 
very eafily when empty, but draw them along on the Plain when loaded, at 
a very good Rate. As foon as the Carriages come to the Brow of the Hill, 
the Horfes are taken off, and one or more of the Wheels lock'd, by the 
Driver, who flands behind to moderate the Motion as he thinks proper. 

When the Carriages are come to the Water-fide, and have been unload- 
ed, they change the Horfes from End to End, fo that the part of the Car- 
riage which went before defcending, becomes the hind-part in afcending 
the Hill, which avoids the Trouble of turning with thefe Wheels. 

Thefe Carnages are loaded at the Quarries, and unloaded at the Water- 
fide, by means of a very good and curioufly contriv'd Crane, fully delcrib'd 
by Dr. J.?. Defaguliers y in his Courfe of Experimental Philofnphy^ Left. III. 

IT- 

N. B. Mr. Allen, to whom I am obliged for a full and thorough Sur- 
vey of thefe Carriages , told me^ that one of them^ when compleatly fi- 
mfhed, and ready to be'ufed, flands him in upwards of 30 Pounds: 
which 1 thought proper to mention as a very reafonable Price conjider- 
ing the good and workmanlike manner in which every thing is per* 
formed, 

Tho' 




mental Phikfophy. 



O *5 



Tho' Mr. Lately eh Defcription is very intelligible, and his Draughts Annotat. 
extreamly well done, yet, to make every thing ftiirplainer, I have add- Left, IV, 
ed Letters to his Draughts, and the following References. iJ~\r\j 

References to the Figure of Mr. Allen* j Carriages and their 

fever al Parts. 

Plate 2 1 * Figure 4* 

ABCDIIIIHFEG. The Body and Bottom of the Carriage, without 
the Sides, which are put on upon occafion in the Place BDHF and fatten- 
ed by means of the Hooks ggg 7 and the Latches e f 

IIII. The crofs Pieces on the Bottom to ftrengthen it. 

MN. Strong Pieces of Timber under the Bottom, 

&. A crofs Piece under the Bottom having an Iron Loop at Top to re* 
ceive the End of a Leaver that preffes on the hind Wheel L 2, to flop it 
from turning round when the Motion is too rapid. 

L, L i, L 2. Three of the four Wheels, the fourth being out of fight 
in this Pofition of the Carrriage, whofe Circumferences have a Flanch on 
the infide that the other part may bear on the Timbers or Waggon-way. 

H. An Iron Roller for the Chain to wind on to hold down the flopping 
Leaver, as it preffes on the hind Wheel 

O, O4, O 1, &c. The Waggon- way, or parallel Timbers laid with a 
Defcent for the Carriages to run down by their own Weight. 

Figure 5* 

FHDB. The right Side of one of the Carriages fix'd by means of the 
Hooks at gggg, and the Latches e^f ihewn in the fourth Figure. 

L. A Fore-wheeel with a round Hole in the Nave to receive a round 
End of the Axis that goes thro' the Piece of Timber P, from another part 
of which the Bolt p is fliot between the Spokes to flop the Wheel from turn- 
ing round, when the Motion is to be retarded. 

Hp. An Iron Rod pufh'd forwards from behind to bolt or lock the 
Fore-wheel abovemention'd. 

L 2. A Hind- wheel fix'd upon, and turning round with the Axis coming 
thro 5 the Piece of Timber the end of which Axis is made fquare for 
that Purpofe. 

R K. A Leaver, whofe End goes thro' an Iron Eye on the Timber K 3 
having there its Center of Motion, with the Coinpafs-piece qq to prefs on 
the upper part of the Wheel L 2, to flop it upon occafion, from turning 
with the Axis. 

H. A Roller on which is wound the Chain HR which pulls down the 
End of the Leaver at R and keeps it in its place, to prefs hard 'upon the 
Wheel at qq. 

G 2, O i. The Waggon-way which fupports the ftrong part of the Cir- 
cumference of the Wheel, while the Flanch or larger Circumference of 

Nn 2 each 




Annotat. each Wheel falls on the infide of the Timber^ that the Carriage may 
Le£t* IV. no * j l * m P or run out of the Way. 

. Plate 22. Figure i. 

This Figure drawn by a larger Scale {viz.. of 10 Inches to an Inch) 
fhews the Elevation of the hind-part of one of the Carriages, with the 
Profit of the Wheels, 

FHGE. The End of the Carriage behind bearing upon four Timbers^ 
whofe Ends are leen here. 

fgy e g : Ends of the Sides book'd oa at g 9 g, and latch'd at /and e* 

H hri 9 and Qhri. A Roller with its Winch, and Ratchet and Latch, 
to receive the Chain that draws down the Leaver or Jig-pole. The Chain 
goes on the Part H,or G, the Holes to turn the Axis of the Roller with an 
Iron Hand-lpike arefeen at hh y the Ratchet at ii 7 and its Catch atr, r. 

Ik, Ik. Two perpendicular Iron Bars, whole lower Ends kk fh@ot for- 
ward each an horizontal Bar (not reprefented here, but Ihewn in the laft 
defcrib'dFigure at H/>) to bolt either of the Fore- wheels fingly, or both at 
once. 

L 2, L4. The Se&ions of the two Hind- wheels, with their Flanches 
mm, mm, and bearing Parts nnn 9 nnn\ the left Wheel receives the fquare 
End of the Axis QJn a Iquare Hole fo as to turn with it, and the right 
Wheel has a round Hole to receive the End of the Axel at P which is 
round alfo> fo that this Wheel can turn round without turning the Axel 
P S Q_ along with it. 

O O 4. Shews the SefHon of the Timbers or Waggon- way - 7 where 
staay be feen the manner of the Wheels bearing on the Timbers at nn % nn, 
whilft the Flanches mm 7 mm, come down to keep the Carriage in its 
Place. 

Q_t, P 1. The croft Timbers thro' the Bottoms of which the Iron Ax- 
els of the Carriages pals, which are fix'd up under the Carriages by Pins 
and Nuts here repreiented by priek'd Lines, 

Figure 2. 

Reprefents one of the Iron Axel-trees S, whole end Q_at the right Hand 
is Iquare, the other end at the left Hand being round, with an Hole for 
the Linch Pin at each End* 

Figure 3. 

Shews the Se&ion of the Hind-wheel on the left Side, or the Fore* 
wheel on the right Side, with a Iquare Hole the Rim of Circumference 
of the Wheel n n 7 and the Flanch mm. 

Figure 4. 

Shews the right Wheel behind or left Wheel before, mark'd with the 
fame Letters except P, which ihews the round Hole to receive the round 

end of the Axis, 

Figure 



A Courfe of Experimental PhUofbptjy 2 79 



Figure 5, Annotate 
Shews the Catch r, and the Ratchet /• Le£L IV* 

Figure 6* 

Shews one of the perpendicular Rods 6f thefixth Figure, whofe Handle 
is at / and the bottom or open End is to join to one of the horizontal Bars 
which flioots a Bolt in between the Spokes of one of the Fore- wheels. 

. Plate 23, Figure 1. PL 2,3. F,)u 

This Figure represents the upper part of the Timber under the Carriage 
between the Fore-wheels, thro' the lower part of whofe Ends the Axel- 
tree paffes, and in the Subftance of which is let in the Machinery for flop- 
ping the Fore-wheels, where the two Bolts A B and CD are feen, which 
may be feparately jfhot out to the right or left Hand thro 5 a fquare Staple P 
or Q_, and refting on one of the crofs Pins e f E F or G H, g b, by means 
of the horizontal Bars IK already delcrib'd, one of which is to be feen in 
the 5th Figure of Plate 21, mark'd H />, and the Ends of both of them 
are feen in this Figure. The Bolt A B on one Side is reprefented as ftiot 
out between the Spokes of the Wheel, and the other is in its ufual Place, 
where it does not touch the Wheel. N. B. Pulling back the Bar L I unbolts 
B A, by means of the Elbow LN B, and pufhing forwards the Bar KM 
bolts C D, by means of the Elbow M N C. 

Figure 2. pl R ** 

The fecond Figure fliews an End of the Timber or the Section of the Ma- 
chinery to move the Bolts as cut acrofs one of the Bo^ and at right Angles 
to the Axis at A, where is feen the Hole P over th^Kxts, and the prick'd 
Lines E F fliews the Pin or Shaft of the Screw on which the Bolt Aides 
as it comes out of its Staple. 

Figure 3. PL &3* F* 3* 

The third Figure reprelents the re&angular Elbow-Piece, fuch as BLN 
or CN M of the laft Figure, where is feen the Center of Motion round 
the Pin N,the End L receiving the protruding End of the horizontal Bar, 
and the End B receives the End of the Bolt to throw it forward as at B 
Fig. 2, or draw it back as at C in the fame Figure. 

Figure 4. t PL 2.3. F, ^ 

The fourth Figure reprefents the Iron-work about the End of the Tim« 
ber at III with the Holes for the crofs Pins, the Bolt B A and Staple R 

Before I begin my next LeRure^ it may not be improper to give an JccomiS 
of a Man of wry great natural Strength who lives now here in London, and 
pews fever al furprizing EffeSls of his Strength. I fhould indeed have given an 
Account of him in the qth Annotation; but I was unwilling to do it upon common 
Report , till I had feen him my felf 7 which 1 only did fince the laft Sheet was 



2oo A Courfe of Experimental Philofophy. 



Annotate Thomas Topham, born in London, and now about 3 1 Years of Age, five 
Lett, IV.'Fooc ten Inches high, with Mufcles very hard and prominent, was brought 
w<Vv up a Carpenter, which Trade he praftifed till within thefe fix or feven 
Years that he has fhew'd Feats of Strength 5 but he is intirely ignorant of 
any Art to make his Strength appear more furprizing: Nay, Ibmetiines he 
does Things which become- more difficult by his difadvantageous Situation 5 
attempting, and often doing, what he hears other ftrong Men have do^e, 
without making nfe of the fame Advantages. 

About fix Years ago he pnlfd againft an Horfe, fitting upon the Ground 
with his Feet againft two Stumps driven into the Ground, but withopt the 
Advantages reprelented by the- fit 'Jit Figure, Plate 19 for the Horfe pull- 
ing againft him drew upwards at a con fide rable Angle, flich is represented 
in the 2d Figure of that Plate, when h N is the Line of Tra&ion, which 
makes the Angle of the Traftion to be NhL: and in this Cafe his 
Strength was no farther employed than to keep his Legs and Thighs 
ftrait, fo as to make them ad like the long Arm of a bended Leaver, re- 
* Pl.19. F. 2.prefented by L h on whole End h the Trunk of his Body refted as a 
Weight, againft which the Horfe drew, applying his Power at right Angles 
to the End / of the fhort Arm of the faid Leaver, the Center of Motion 
being at L at the Bottom of the Stumps /, 0 (for to draw obliquely by a 
Rope faflten'd at h is the fame as to draw by an Arm of a Leaver at / L, 
becaufe / L is a Line drawn perpendicularly from the Center of Motion 
t Ann. 5. to to the Line of Dire&ion j- h N) and the Horfe not being ftrong enough to 
Left. III. p. ra ;f e the Matfs^ Weight with fiich difadvantage, he thought he was in the 
I42e right Pofture for drawing againft an Horfe - 0 but when in the lame Pofture 

he attempted to draw againft two Horfes, he was pulPd out of his Place by 
being lifted up, and fed one of his Knees ftruck againft the Stumps, which 
fhatter'd it fo, that even to this Day, the Patella or Knee-pan is fo loofe 3 
that the Ligaments of it feem either to be broken or quite relaxed, which 
has taken away moft of the Strength of that Leg. 

But if he had fat upon fuch a Frame as is reprefented in the firft Fi- 
*Pl.i9.F.i. gtire * and defcrib'd in Page 25^, 258 and 259, he might (confidering his 
Strength) have kept his Situation againft the pulling of four ftrong Horfes 
without the leaft Inconvenience. 

The Feats, which I faw him perform a few Days ago, were the following* 

1. By the Strength of his Fingers (only rubb'd in Coal-afhes to keep 
them from flipping) he roll'd up a very ftrong and large Pewter-dilh. 

2. He broke feven or eight fhort and ftrong pieces of Tobacco-pipe with 
the Force of his middle Finger, having laid them on the firft and third 
Finger. 

3. Having thruft in under his Garter the Bowl of a ftrong Tobacco-pipe, 
his Legs being bent, he broke it to pieces by the Tendons of his Haan% 
without altering the bending of his Leg- 

■a. He broke fuch another Bowl between his firft and fecond Finger, by 
preffing his Fingers together fide-ways,, 5. He 



A Courfe of Experimental Philosophy. 281 



5. He lifted a Table fix Foot long, which had half a hundred Weight Arniotat 
hanging at the End of it, with his Teeth, and held it in an horizontal Po-Le£t. I V« 
fition for aconfiderable time. It is true the Feet of the Table t 'efi h >d againfi : L/"V%J 
his Knees ^ but as the Length of the Table was much greater than its Height^ 

that Performance required a great Strength to be exerted by the Mufcles of his 
Loyns, thofe of his Neck, the Mafieter and Temporal {Mufcles of the J ^wtyi 
befides a good fet of "Teeth. 

6. He took an Iron Kitchin-poker, about a Yard long, and three Inches 
in Circumference, and holding it in his right Hand he ftruck upon his bare 
left Arm, between the Elbow and .the Wrift till he bent the Poker nearly 
to a right Angle. 

7. He took fuch another Poker, and holding the Ends of it in his Hands, 
and the Middle againft the Back of his Neck, he brought both Ends of it 
together before him $ and, what was yet more difficult, he pull'd it almoft 
ftreight again j becauft the Mufcles which feparate the Arms horizontally 
from each other are not fo ftrong as thole that bring them together. 

8. He broke a Rope of about two Inches in Circumference which was 
in part wound about a Cylinder of four Inches Diameter, having faften'd 
the other End of it to Straps that went over his Shoulders; but he exerted 
more Force to do this than any other of his Feats, from his awkwardnefs in 
going about it } for the Rope yielded and ftretch'd as he flood upon the Cy- 
linder lb, that when the Extenlors of the Legs and Thighs had done their 
Office in bringing his Legs and Thighs ftrait, he was forc'd to raiie his 
Heels from their Bearing, and ufe other Mufcles that are weaker. But if 
the Rope had been fo fix'd that the Part to be broken had been ihort (in 
the Manner explain'd in the 7th Annotation of this Lefture) it would have 
been broken with four times lefs Difficulty. 

9. I have feen him lift a rolling Stone of about 800 ft with his Hands, 
only (landing in a Frame above it, and taking hold of a Chain that was 
faften'd to it. By this, I reckon he may be almoft as ftrong again as thofe 
who are generally reckon'd the ftrongeft Men, they generally lifting no more 
than 400 lb in that manner. The weakeft Men, who are in Health and 
not too fat, lift about 125 jfe, having about half the Strength of the 
ftrongeft. iV". B. This fort of Companion is chiefly in relation to the 
Mufcles of the Loyns - 7 becaufe in doing this one muft ftoop forwards a lit- 
tle. We muft alfo add the Weight of the Body to the Weight lifted. So that 
if the weakeft Man's Body weighs 150 lb, that added to 125 ffo makes the 
whole Weight lifted by him to be 275 lb : Then if the ftronger Man's Body 
weighs alio 150 lb, the whole Weight lifted by him will be 5 50 it, that is 9 
4001b, and the 150 ft> which his Body weighs, fopharn weighs about 
200 which added to the 800 lb that he lifts, makes 1000 lb but he 
ought to lift 900 lb, befides the Weight of his Body, t6 be as ftrong again 
as a Man of 1 50 ft Weight who can lift 400 lb* 

Now as all Men are not proportionably ftrong in every Part, but lome 
are ftrongeft in the Arms, fome in the Legs, and others in the Back, ac- 
cording to the Work and Exercife which they ufe, we can't judge of a 

Man's 




Annotat Man's Strength by lifting only % but a Method may be found to compare to* 
Led. VkS^her Strength of different Men in the lame Parts^ and that too with* 
iy^/^sj out [training the Perfons who try the Experiment, 

Here follows the manner of doing it, which was communicated to me hy 
Richard Graham, Efa F. R. S« to which I made fome [mall Additions* 

Plate 23 y Figure 5. 

A BCD is a ftrong Frame of Wood with an Hole thro' the upright 
Piece D at D big enough to receive an Iron cylindrick Bar of an Inch 
Diameter or fomething bigger, a ftrong Iron Plate being fix'd on each Side, 
that the Iron may not gull the Hole. This Bar has a Square upon it, whofe 
Side is about an Inch and one eighth to receive the two feparate and une- 
qual Arms of a bended Leaver D F and D E j and then a ftrong Nut' d is 
Icrew'd over them at D to keep all tight. The Arm DE, which as a Stil- 
yard is to carry a great Weight W, is kept from falling below an horizon- 
tal Pofition by an Iron Pin at K, which flops the fliort Arm DE from in- 
clining towards G 5 but both Arms are moveable round the Axis D towards 
e or N. The Arm D F has a round crofs Bar at top about fix Inches long, 
as may be feen in its feparate Reprefentation d f To the upright Tim- 
ber A B is made fall the Iron L N, with a Croft alfo at Top (See n I) and 
Holes for Iron Pins to fatten it in its Place. There is alio another ftrong 
piece of Iron HGI faften'd to the Timber that carries the Leaver by a 
ftrong Wood Screw at I, and the Pin K going thro' its Wings and the Tim- 
ber. Seeks feparate Figure at hgl. S is a Collar to put on when you 
don't ufe the upright Arm of the Leaver. M is the Center of Gravity of 
the Stilyard DE. 

i. To try one's Strength by means of the Machine $ with the left Hand 
take hold of the round part of the Crofs at N, and of the round part of 
the Crofs at F with the right Hand, and bring your right Hand towards 
the left in the Direction of FN which will move DE and raife the 
Weight W. When you can juft raife it up fo as to make FD quit the 
Pin- at K, the Force of the Arms will thus be found. Multiply the Weight 
W (fappofe an half hundred, or 56 lb) by its Diftance from the Center 
WD (which we will fuppofe here 15 Inches) which will give 840 for the 
Momentum of W on the Stilyard: Then add to it the Momentum of the 
Stilyard it (elf, which you will have by finding what Weight can draw up 
the Stilyard by its Center of Gravity, namely the Weight W (Tig* <5.) 
which draws it up by a String going over the Pulley C$ and multiplying 
that Weight by MD its Diftance from the Center (which we will here 
fuppofe 10 Inches) you will have 6o y which being added to 840 make the 
Sum 900, and that Sum, divided by FD the Diftance of the Power, will 
give 90 ftj for the Force of the Man's Arms who applies his Hands at F 
and N. If another Man raifes double the Weight at W -f- fo much Weight 
as will anfwer to double the Weight of the Stil-yard at M, he is twice as 

ftrong 



A Courfe of Experimental Philofophy. £83 

ftrong. The removal of the Weight W toward E will alio ferve to ftew Annotate 
how much the Force is greater, inftead of adding Weight at W. -f* Le£b IV* 

The lame way may be found what Force the Arms can exert in pulling v_>"~v~n^ 
from each other, by applying one Hand at F and the other at H.tPl-*}.F.$„ 
And to try the Force with which Topham bent the Poker bearing behind 
his Neck j a Man muft put a Strap round his Neck, which muft be faften'd 
to F ; then the Head being plac'd oa the Side N of N L, with both his 
Hands he muft take hold of the Crofs at N and pufh forwards with his 
Hands, all the while pulling backwards with his Neck, to bring F to- 
wards N. 

2. The fixth Figure is another wooden Frame with the upright Timbers 
A B,C O a little farther afunder. * So that a Man may ftand upon theiirong* PU3 F. 6* 
Plank F G, and with the Girdle and Chain thro' the Hole H pull up the Stil- 
yard D E by the Hook I, which Stil-yard in this Cafe has not the upright 
Piece F D, but inftead of a bended Leaver becomes a Leaver of a third 
kind, where DI is the Diftance of the Power, and D W the Diftance of 

the Weight-, and therefore ^ * ^ ^L w . ® w m 5 e the abfolute 

Weight that is lifted, or Force of the Mufcles extending the Legs. But 
here the Weight of the Trunk of the Body muft be added, and confider'd 
according as feme Men are heavier than others. N. B. The Notch f K bin* 
ders the Leaver from falling below the horizontal Situation j andw drawing 
over the Pulley C fhews how the Leaver a£Is at its Center of Gravity: So 
that when w is hung on 9 the Leaver is to be looked upon as an Inflrument with" 

out [might. tH.*3.F.7- 

{. The feventh Figure *{- has the Stil-yard at D E with a wooden Cy- 
linder of an Inch and an half, or two Inches in Diameter, upon its Axis 
continued behind at DF, which Cylinder is drawn feparately at df 9 and 
its Iron Axis at g h, and the Nut at i. t PI.23.F. 8« 

4. The eighth Figure ^ reprefents a Machine to try the Strength of the 
Fingers-, in which, when you thruft the Fore-finger under G, and the 
third Finger under H, which are fix'd Points, the middle Finger may pufh 
upon N to lift a Weight at W, in the fame manner that Topham breaks 
the pieces of Tobacco-pipes. If the Hand being held with the Palm up* 
wards, the two firft and two laft Fingers be thruft in under G and H, and the 
Thumb prefles upon N ; that will fhew in what manner the tops of Pewter 
Pots and Silver Tumblers have been fqueez'd together by Men very ftrong 
in the Fingers $ and thus will be fliewn the Strength that any Man can exert 
for fuch an Attion, ©V. 



Oo 



LECTURE 



LECTURE V. 



Concerning Sir Ifaac Newton's' three Laws of Motion. 

r* p iJU |[ ll, t H ERE are feveral Organs 'jDf Mruments^ which may 
|| be callM Mechanical, or enumerated among the In* 
B ftruments, commonly, but erroneoufly, calPd meek am* 
cal Towers which I purpofely omitted (or only men- 
tion^ without explaining their manner of a£ting) in the third Lec- 
ture ; becaufe the Knowledge of the Laws of Motion is neeeflary 
for undemanding upon what Principle they a£t: And fochare the 
battering Ram> y the Hammer or Mall, the Fly y the circularlPen- 
duhm y the Blkpg^ aaad thr Bom or Mprmg.- 

I shale therefore in the firflr place cdnfidter thofe Latvsj, and 
draw feveral GoroUaries or Confequences from them, which I fliall 
illuftrate by Experiments, and apply them among dthef Things to 
explain the Ufe of thofe InftrumentSe 

LAW I. 

Every Body perjemr&s in- & State of Meft y or of uniform Mo- 
tion in a right Line v unlefs it be comfeWd to change that 
State by Forces imp *efs } d thereon. 

5v There is in all Matter (whatever kind* of Body it be fhap'i 
into) an Inactivity whereby it refifts any Force that endeavours to 
make it change its State, in proportion to its Quantity of Matter ; 
and this- is calFd the Vis Inertia or Force of Inactivity. For it is 
as impoffible for a Body to go into Motion of it felf from Reft 5 as 
to change its Shape from one Figure to another. This is evident 
to Senfe, and I believe no body doubts of it ; but the fecond part of 
this Law does not appear fo evident without a little Attention. 



A Courje Experimented Philofophy. 



We fee plainly that there muft fee fame extrinfecal Agent or Pow- LeSL V. 
er not eflential or belonging of neeeftlty to the Body, to put it in- L^^%J 
to Motion : but we don't fo readily perceive that a Body in Motion 
would eontinue to move for ever without the action of an extrinfecal 
Agent ' ? becaufe we fee Bodies here on Earth gradually lofe their 
Motions, and for want of attending to all the Caufes that deftroy 
the Motion of Bodies, we often imagine that Motion languishes and 
at laft quite perifhes of it felf. But if we confider what external 
Caufes retard and deftroy Motion, we fhall foon perceive that if 
thofe Caufes were removed, a Body once put into Motion in any Di- 
rection woii'd continue in that Motion and Direction for ever. 

A Stone thrown forwards with the Hand goes on with the Mo- 
tion that it has received from the Hand, and wouM continue in 
that State of Motion for ever, if there was neither Air nor Gravity. 
When we confider the Refiftance of the Air, it is evident that the 
Body in going forwards muft remove the Parts of the Air to make 
it felf way ; and as it muft communicate Motion to thofe Parts which 
it removes ; fo much Motion as it eommunieates,fo much it muft lofe ; 
fo that after fome time and having gone through a certain Space it 
muft hang in the Air immoveable, that is, if nothing but the Air 
a£ted upon it. But befides the Air, Gravity (which is a Force pufh- 
ing downwards) alters its Dire&ion and brings it gradually to the 
Ground/This Endeavour which every body has to continue in its State 
of Motion does not feem to fome to be properly CalPd a Force of 
Inactivity (Vis inertia) but when we confider that the Body is 
purely paffive, neither augmenting nor throwing off any of its Mo- 
tion of it felf, we fhall find it to be entirely ina£tive even in that 
State, Thus when we ftand by a River Side and obferve a live Fifli 
carried down the Stream, he is wholly inactive in that Motion, and 
continues in that Motion all the while he isina&ive : it muft be an 
Action exerted (equal to the Force of the Water) that will make, 
him come to Reft and appear fo in refpefit of the Spectator on the 
River Side. 

Suppose a Man exerts a certain Force to roll a Bowl on a Bowling- 
green neither mow'd nor rolPd, and can only throw it 20 Yards with 
that Force ; when the Green is mow'd, he mail with the fame Force 
throw it farther, 30 Yards for Example; then if the Green be rolPd 
as well as mow'd, the fame Force may throw the Bowl (for Exam- 
ple) 40 Yards ; and ftili if more of the Obftacles are taken away, 

O o 2 the 



286 A Courje of Experimental Philofophy. 

Led. V . the Bowl will yet go farther ; whence one may eafily conclude, that if 
'✓w the Plane on which the Bowl rolls could be made perfectly fniooth 
and mathematically true, the Bowl truly fpherical, and the Refinance 
of the Air wholly taken aWay, the Bowl would for ever roll (or 
rather Hide) on that Plane if it was infinitely extended, 

f . We have fhewn by a Quotation from Sir Ifaac Newton (L. 
3 . N 3 . 85.) that if a Body be acted upon by two Forces whofe Di- 
rections make any Angle, the Body will move in the Diagonal of a 
Parallelogram, two contiguous Sides of which reprefent (by their 
Lengths) the refpe&ive Quantity of thofe Forces, and (by their 
Inclination) their Directions: and alfo that the Body will go thro* 
the whole Diagonal by the Action of the faid two Forces, in the 
fame Time that it wou'd have gone thro' either of the contiguous 
Sides, if only one of the Forces had acted upon it. 

This is not fo readity conceiv'd by thofe who are not accuftom'd 
to mathematical Reafoning; becaufe, while they obferve the Acti- 
on of one of the Forces, they do not attend to the other : but it 
will appear very evident, by confidering fuch Cafes wherein the 
Space in which the Body moves is carried in a different Direction 
from that which the Body appears more immediately to be mov ? d 
*PU3,F.io.in. As for Example, let us fuppofe TS ( * TL 23. Fig. 10.) to be 
a Tragfcbuit or 'Dutch travelling Boat (I mean the Plan of it) H b 
g G, the Canal in which the Boat goes in the Directon Tj, and A 
and B two Perfons fitting over againft one another in the Boat. Now 
let us fuppofe the Perfon at A tolling any Body, as for Example, a 
Ball, to the Perfon at B, and fo reciprocally : all the People in the 
Boat will confider the Ball fo tofs'd as only moving in the Line A B, 
whether the Boat Hands ftill or goes on along the Canal, th®' there 
be but one Force acting upon the Ball in the Direction A B when 
the Boat ftands ftill, whereby it really moves in that Line ; but when 
the Boat goes along, another Force in the Direction A a does alfo 
at the fame Time act: upon the Body, which by that compound 
Action is really carried in the Line A B, tho' the Perfons fitting by 
fancy the Ball to go ftill in the Line Kb, becaufe they are carried 
along too,and forget that theForce which draws the wholeBoat does 
alfo carry the Ball along, which is a part of it, as well as themfelves. 
Now this will be evident to the Sight of a Man that ftands upon the 
Bank at C ; for when the Boat ftands ftill he looking towards D on 
the oppofite Bank, fees the Ball move (as it really does) in the Line 

AB. 



A Courfe of Experimental Philofophy. 2 87 



AB. But when the Boat moves and goes from the Pofition T S Left. V. 
to the Pofition t s in the fame time that the Ball moves acrofe from ^\T^J 
the Perfon at A to the Perfon at B, it is plain (and will be feen by 
a Man on the Bank at C) that the Ball moves in the Diagonal Line 
Ab, becaufe the Perfon who was at B does not receive it till he is 
carried to b by the Motion of the Boat ; which his Oppofite (be- 
ing at the fame time carried to a) does not attend to, tho' tha 
Thing be fo vifible to the Man at C. Yet if the Man at C ftood 
upon a Plank at AC faften'd to the Boat, being then carried along 
from C to c , he would not diftinguifh between the Line A B and 
the Line A but (when he came to c) fuppofe that the Body had 
mov'd in the Line ab y which he would miftake for AB; unlefs 
looking over the Canal, he fliou'd confider that he no longer faw 
the Point D but the Point d. Thus in a Ship, if a Man ftanding 
on the Deck near the Maft toffes up a Stone to another who ftands 
on the round Top, or receives a Stone dropp'd from thence, the 
Stone will move parallel to the Maft (fuppofing the Maft upright) 
whether the Ship be at Anchor or under Sail ; tho' in the firft Cafe 
the Stone moves perpendicular to the Horizon, and in the laft Cafe 
oblique to it as it rifes or falls in the Diagonal of a Parallelogram, 
whofe contiguous Sides reprefent the two Forces a&ing upon the 
Body, the one perpendicular, and the other parallel to the Horizon ; 
juft as in the laft Inftance, the two Forces AB and Aa a&ed upon 
the Ball horizontally projected in the Boat. 

N. B. Whether the Boat goes f after or flower (in which Cafi 
A b becomes longer or porter ) the Ball will perform its dia- 
gonal Motion in the fame Time ; for fince the Force A B 
continues the fame] all that is done by the lateral Force 
A a. is only to make theBaU come to a different Toint of the 
Lin eBn as m or h or n inftead of B, while the Force A B 
in the fame Time carries it crofs the Boat, or from fome 
■part of the Line A a to fome fart of the Line B b. 

I have been the more prolix in this Explication, becaufe I have, 
met with a great many Perfons of good Senfe, who for want of 
Attention have not been able to conceive this compound Motion, 
on which all Mechanicks are founded. For this Reafon I have lub- 
join'd variety of Experiments to the fame Purpofes, becaufe if one 
don't, another may, convince. 



EXPE« 



288 4 Comje of Experimental Philofophy. 

^^"^ E x p e r i m e n T I. Tl. 23. Fig. 1 r. 

Pi. a 3 . F. 11. The Machine of Plate 2 3. Fig. r t. confiftsof abrafs Plate ABCD 
upon which another Plate I K L M Aides forwards and backwards 
in the Direction TS or ST between the Rulers AD and BC un- 
der the Edge of two other Rulers E E and GH, of which E F is a 
little Rack with Teeth to receive the Teeth of the Wheel N, which 
is faften'd to the Plate IMKL by the Cock NO, and turns round 
its Axis N as the faid Plate is pufh'd forwards and backwards. The 
Wheel in its Motion along EF carries another Rack P Q at right 
Angles to the former either to the right or to the left, according as 
the Axis of the Wheel at N is pufh'd in the Direction TS or ST. 
This laft Rack has an Arm S R with a little Socket at R to receive 
a black Lead Pencil, which according to the Motion of the End R 
will draw a black Line upon the Paper on which the Machine is to 
belaid. 

There muft be drawn upon the Paper a Square e fgh, one of 
whofe Sides is equal to the Diftance between the Edges of the 
Rulers A D and B C. Then having pufh'd up the Wheel N as far 
as it will go, lay the Machine upon the Paper, fo that its End AB 
may be parallel to g h one fide of the Square abovemention'd, at fuch 
a Diftance as to have the Point of the Pencil fall upon the Point e, 
and the Edge of the Rack P Q. over the Line ab: then with one 
Hand preffing down the Plate ABCD of the Machine at'T, to 
keep it immoveable upon the Paper, pull d@wn the Cock N O in 
the Direction ST a Length equal to eg; and the Pencil, inftead of 
defcribing the Line eg, will clefcribe the Diag©nal Line e h, becaufe 
as the Wheel in its Defcent is turn'd round by the Rack EF, it 
throws the Rack PQ^ to the right, juft the length of e f, by means 
of the Teeth in the faid Rack, and the Slit in it which lets it go late- 
rally alpng the Pins IM by the Aftion of the Wheel, while the faid 
Pins bring it perpendicularly down from the Line 4 b to the Line de. 
And to fhew that the Diagonal is defcrib'd in the fame time that the 
Side eg wou'd have been defcrib'd if there had been no lateral Mo- 
tion ; take off the Wheel, and then the Pencil's Point will defcribe 
the Line eg, while the Cock is drawn down the fame Length as 
before, or pufh'd up again. This fhews that it is the fame thing 
for a Body at e to be acled upon by two Forces in the Direc- 
tions e f and eg, as to be carried from the Line e g t© the Line 



fit, at the fame tmM ttet k wfe$<M$$ti dbw& from the Line <?/ to Le£LV. 
the Line 4 u^V%j 

E X- P E R I M E N T ft. 2^1 23. F/g. 1 2- 

¥mE 1 2 th Figure of Pfete 23 is * fqtiare Frame of Wood, of Pi. 23. F. u; 
Which the part C D-B E is to be fet up on its Side BE, whilft the 
other part of it c d e b is drawn out of its Groove into the Pbfitioii 
d& te\ by which means the Ball A is made to defcribe the Diagonal 
A a afcending, and the fame Diagonal defcending is defcrib'd when 
the Aiding part is pufh'd back into the Frame in the Dire&ion S d. 
There is a Wire Ac JixM to the Aiding part for the Ball to move 
up and down-on,' and a String he which goes thro' an Hole in the 
Pieces dc and D C, fo as to have its End faften ? d at C; by which 
means the Ball muft rife when d $ e e is drawn out laterally ; and 
it falls back again by its ownWeight when d ze is pufhM in again : 
arid when d£ ee is left in its containing Frame, the Ball will rife 
and fall by pulling or letting go the String C cb. If the Wire AB 
be confider'd as a Rope parallel to the Mafl: of a Ship, what we 
have faid of a Body let fell' from* the round Top of the Maft and 
moving parallel to the Maft (whether the Ship be at Anchor or 
i»der Sail) by one, 0^ tWo Forces a£ting upon it, will be Muftra- 
ted/. 

Wut as I have heard 'fottie 1 b^e^; tliat tMs> and the laft men- 
tion^ Machine,, did indeed^ by the Contrivance of them, make a 
Body move in a Diagonal ; but they did not prove that Nature 
a£ted that way ; I have made the Thing evident to Sight by the 
following 

E x. p e r 1 m iNT llL TL 23. Big. 1-3. 

The round Table GEFD Hands upon: a twp&F> and has aii.pu 3 .F. 13. 
Hole on each Side of its Center half way from the Circumference, 
at A and B. At right Angles to the Line that goes thro 7 A G B is 
drawn a Diameter DE, and from feveral Points of that Diameter 
equally diftant from the Center on each Side, are drawn the 
Rhombs or equilateral Parallelograms, DAEB, dAcB, and <T A 
e The Ball D has two Strings faftenM to it at the fame Pointy 
and thole Strings being carried thro' the Hole AB, have hanging at 
their End two equal Weights W and X, which by the joint Force 




Led. V. of their Defcent will bring the Ball D to reft upon C the Center 
v*vv>- of the Table, whilft the parts of the Strings on the Table are in 
the Line ACB. If the Ball D be pulPd back to <P,d, or D (whereby 
the Weights W and X will be rais'd up, and the Strings will lie up- 
on and have their Dire&ions in the contiguous Sides of one of the 
Parallelograms) as foon as you let it go again, it will run in the Line 
DE which is the common Diagonal of all the Parallelograms; as 
may be beft perceiv'd by holding one's Finger or a Wire at the Cen- 
ter C, which the Ball will ftrike in its Motion. Here it is plain 
that the natural Gravity of the Bodies W and X is the only Force 
(divided into two equal Tart sj which a6ls upon the Ball X) y and 
that whether the T)ire£lions of thofe Forces be at acute^ right, 
or obtufe Angles, the Ball is fiill carried in the diagonal of a Pa- 
rallelogram of equal Sides, reprefenting equal Forces. But if 
one of the Weights as W, be taken as heavy again as the other \ 
the Ball from D ? d, or will run in a Direction between AandC > 
and not run over the Center till you let it go from F, in which 
Cafe the two Strings will make two contiguous Sides of theTaraU 
lelogram FAGB, whofe Proportion to each other is alfo as Two 
and One i the ^Diagonal being FCG, which pajfes thro* the Center. 

It was objected to Galtlao when he aflerted the Motion of the 
Earth, that if the Earth did turn round from Weft to Eaft, a Can- 
non Ball fliot upright, would not fall down in, or near the Place from 
which it was fhot (as we fee by Experience it does) but move to the 
Weft according to the fpace of Earth that had been carried towards 
the Eaft, during the Rife and Fall of the Ball ; which he anfwer'd, 
by faying, that the Ball is a&ed up^n by two Forces, One, that of 
the Powder which throws it up, and the Other, that of the Earth 
which carries it to the Eaft, making it in its Rife defcribe a Dia- 
gonal Line towards the Eaft, and from the upper End of that Dia- 
gonal, another Diagonal Line alfo towards the Eaft in its Fall. He 
alledg'd the Cafe of the Ship that we have already mentioned. But 
npthing will make the Thing fo plain as the following, 



Exp e» 



A Courje of Experimental Philofophy. 291 

Experiment IV. TL 24. Fig. 7. s^v-x^ 

To an horizontal Piece of Wood GH, fix'd about ro Foot above pi. z\ 0 f. ?, a 
the Floor of my Room, I fcrew'd the two Hooks S s 9 and by means 
of four Strings hung on the faid Hooks, the brafs Plate or flat Pen- 
dulum ABCD, which (by reafon of the Diflance of the Strings 
at their Points of Sufpenfion Ss) performed its Vibrations in a cir- 
cular Arc over the graduated upright wooden Plane E F which flood 
under it, the Center of the Pendulum never moving out of the 
Plane of the Wood as it vibrated in the Dire&ion E , or back a- 
gain, at the Diftance of about nine Foot from the Piece G H Over 
the two Pullies I, K, fcrew'd into the upper Side of the Piece GH, 
ran the String LK I W, whereby the Weight W might be let down 
upon the Pendulum A B CD, or lifted off from it at pleafure ; there 
being an Hole thro' GH, juft under the Circumference of the 
Groove of the Pulley I. 

Let the Pendulum (the Weight W being upon it) be drawn out of 
the Perpendicular to E, and then, when it is loosed, it will vibrate 
towards F, and fo back again towards E, &c. for a confiderabie Time. 
During that Motion, if by pulling the String at L the Weight W 
be lifted off of the fwinging Plate, and then let down again, it will 
always fall upon the fame Part of A B C D, tho' A B C D be mov'd 
a great way out of its Place diiring the Time that the Weight W is 
off of it ; and that, at whatever Part of the Vibration W is lifted off, 
and at whatever Part of it, it is received again. For tho' the Force of 
the Hand pulling the String is the Caufe of the Rife of W, and Gra- 
vity the Caufe of its Defcent, yet it has alfo another Force a£Hng 
upon it, which moves it in the Arc of Vibration, as Part of the Pen- 
dulum compounded of ABCD and W. Juft fo as any Part of the 
Earth, on which a Cannon is fet upright, is carried from Weft to 
Eafty by the Motion of the Earth round its Axis; the Cannon Ball 
fhot up, befides the Motion received from the Explofion of the 
Powder, has another Force imprefs'd upon it by the Earth's Motion, 
as it is a Part of the Earth, and is carried from Well to E a ft in the 
Air, as well as the Cannon is upon the Earth, fo as to fall down 
again into, or near, the Mouth of the Cannon. 

A Cannon Ball or any other Proje&ile never deftribes a right 
Line in its Motion, but when it is thrown perpendicularly up or 

P p down, 



2^2 



A Cowrfi of Exprntmeiftal PMofi^hy^ 



Lech V. -down) which right Line of Afcent or Defcent is the Diagonal of 
t/vv a Parallelogram, as we have already fhewn ; but when the Body 



calPd a parabolic k Line. No\y this Curve is made up of an infi- 
nite Number of fmall Diagonal Lktes, that continually change as 
the Directions of the Forces alter in the Body ? s compound Motion, 
which is eafily explained from what has bedn faid of the Afition of 
two Forces, and the Confideration of the Acceleration of Motion in 
the Fall of Bodies ; which (as it is a Fa£fc and Matter of Gbferva- 
tion) muft be now taken for tgranted ; tho' we fhan't explain the 
Caufe of it, but in the Explication of the fecond Law of Na- 
ture. 

*pi. 22. F4. Let a Body at A (* Tl. 24. Fig. v.) as for Example, a Cannon 
Ball, be fhot forward in an horizontal Direction A F, fo as to move 
with a determinate Velocity ; for Example 4 Rods in a Second of 
Time, or from A to B. It is evident by the Firft: Law, that it 
muft the next Second go on in the fame Direction thro' the fame 
Space, viz. from B to C, and fo to D, then to E, then to Fy&c. 
It is alfo plain, that if there be another Force whofe Dire£tion is 
at right Angles to the Line A F, as in the Line A L, which is 
perpendicular to the Surface of the Earth, (or to take the thing 
more generally, a Force preffing from the Line A F towards the 
Line L /,) the A&ion of this laft Force upon the Body fetting out 
at A will neither accelerate nor retard its Motion from the Line 
A L to the Line B M, nor from the Line B M to the Line C N, 
nor from the Line C N to the Line D O, nor from the Line D O to 
the Line E P, nor from the Line E P to the Line F f ; but only 
caufe the Body to go thro' different Points of thofe Lines inftead of 
the Points B, C, D, E, F. Now I .lay, 'thar^,\r,;^ v '<?^and'j^ will 
be the Points of the Lines BM, C N, D 0, EP and Ff] which the 
Body will go thro 5 . The Force preffing downwards in the Direc- 
tion AL is the Force of Gravity, by whofe A&ion it is obferv'd 
that Bodies fall with an accelerated Motion, in fuch Manner that 
in the firft Second of Time a Body falls 1 Rod (or i6 l 2 Feet,) the 
2d Second, 3 Rods \ the -d Second, 5 Rods \ the 4th, 9 Rods, &c. 
which Spaces are here exprefsM by A G, G H y HI, I E and KL. 
And if the falling Body, during the Time of its Fall, be afited up- 
on by another Force in an horizontal Direction, as in the Dire&ion 
A F, (or rather from the Line A L towards the Line F / ) that Force 
will not at all difturb the uniform Acceleration of the - Motion of 




the 



A Courfe of Experimental Phikfophy. 293 

the defcending Body, but only make it fall to fome other Point of Left. y. 
the Line L/ (or of the Surface of the Earth) than the Point L, as w-v->J 
for Example to the Point f. 

The feveral Points of the Curve in which the Body moves will 
be thus found. The Body at A is a£bed upon by the two Forces 
A B and A G ; the Lines G b and B b, refpe&ively equal and pa- 
rallel to A Band AG, comgleat the Parallelogram Kb: confe- 
quently the Body muft move in the Diagonal A b. The Body at 
b is aded upon horizontally by the Force b k equal to A B (or 
brought down from B C) and at the fame time by the Force b h 
increas'd by Acceleration from i to 3, and transfer'd from GH to 
b h \ for as without the horizontal Force, it would in the 2d Second 
of Time have carried the Body from G to H (as it is not altefd 
in the Quantity of its Efteel by the horizontal Force) it will there- 
fore be able from b to carry down the Body to h ; but the horizon- 
tal Force b k a&ing at the fame Time, does in the fame Time car- 
ry the Body from the Line b h to the Line k c, as the Force b h 
carries it from the Line b k to the Line h c, and confequently at 
the End of the id Second of Time the Body will be at c where the 
two above-mentioned Lines meet, having defcrib'd the Diagonal 
b c by the joint Action of the Forces b k and b h. The Body at c is 
aded upon by the horizontal Force ci, (== C D) and the perpen- 
dicular Force c i (fo increas'd as to be = H I) at the fame Time ; 
therefore the Body will go in the Diagonal c d. For the fame Rea- 
fon, when the Body is at d it will go in the Diagonal d e of the 
Parallelogram d% e by the joint Action of the Forces d e and 
d k ; and fo from e it will go to / in a new Diagonal, viz. that of 
the Parallelogram e qfl, by the A&ion of the two Forces e $ and 
e /, he. 

S C H 0 L I V M. 

If we had divided the Time of the whole Motion into more, and 
therefore lefs, parts ; we fhould have had more Diagonals from A, the 
Beginning of the Fall of the projected Body, to / the End of it, 
which would have made its way Abe def more curve by having 
niore changes of Direction in it. Now as the Motion of Bodies 
downwards by the Force of Gravity is continually increafing (or the 
Line A G continually becoming longer) and not increafing by Fits, as 
we have fuppos'd it to make: the Adion of the two Forces the better 

P p 2 conceiv'd, 



2p4 A Com je of Experimental Thilojopby. 



Left. V. conceived, there is a continual Change of Dire&ion in the Motion 
of the Body forwards and downwards (or the Diagonals become 
infinitely fmall) fo that it defcribes a Parabola in going from A 
tof. 

This may be illuftrated by the following 



Experiment V. 



PL 
4 



i. 24. f. 3, Xhi Machine reprefented by the ^d, 4th, and 5 th Figure of 
Tl. 24. was contrived by Dv. r sGravefande (Profefforof Mathema- 
ticks and Aftronomy at Ley den) to make this parabolick Motion 
of Proje&iles evident to fight. A B b GF is a folid Piece of Wood 
3 5 Inches high and 2 Inches thick, Handing up upon its End F G, and 
fet upon the Board or flat Piece F E, which has a little fhallo w Pit at 
E to be filPd with foft Clay,- fo that when the Ball B falling from 
B along the curve Surface Bb (which is made very fmooth, or 
fa'cd with Brafs or planifh'd Tin) and defcribing in the Air the 
Farabolick Line b % <P E it may make a Mark to fhew exa&ly the 
Place where it fell. The Piece G (Fi^. 4.) is fometimes to be put 
on upon G E of Fig. 7. where the prick'd Lines reprefent it at G 
§ J ? having alfo 'a Pit to fill with Clay to receive the Mark of the 
falling Ball at f\ The Piece K (JFig 5.) is to be put on over it up- 
on Occafion, where it is reprefented by the prick'd Lines 1 q to 
intercept the falling Ball, and fhew by the Clay in its Pit where the 
Point v, of the Line f % falls. There is alfo an upright Board 
B D E to be taken oft' and on upon Occafion, on which are faften'd 
the 3 Rings r\ r 3 r, thro' which the Ball will move when it de- 
fcribes a Parabola from b to E, the/ Pieces of Fig. 4. and Fig. 5. 
being then removed. 

The Height B C, or the Diftance between the Line A B D and 
the Line C b c d e, is of fix Inches ; and the Height b G is of nine 
Inches, being divided into three unequal Parts, of which the upper- 
moft contains 1 Inch, the next 2 Inches, and the loweft s Inches. 
Now if the Time, in which the Ball falls from b to G, be divided into 
three equal Parts (which we will here call Inftants) the Ball will in 
the firft of them fall the firft Space marked 1, that is, one Inch ; 
and in the next Inftant the Space 3, or q Inches, and in the ;d In- 
ftant the fpace 5, or 5 Inches N. B. This happens on account of 
the accelerated Motion J the Caufe of which we fhall explain in con- 
sidering thefecond Law of Motion. When we let the Ball fall from 

B, and 




hilofephy* • c.pt; 



B, and it rolls down along the curve Surface B it has acquirM Lefit.V. 

fuch a Velocity at b as is able to throw it forwards (double the Di- u^rvj 
fiance B C or Height from whicMt fell) by an uniform Motion, viz. 
from b to e, in the horizontal Line bcde, if it was not fore -d out 
of it downwards by the ■ A&ion of Gravity • but Gravity neither 
accelerates nor retards its Motion forwards, only makes it come to 
the Point Eiinftead of the Pointy in the fame perpendicular Line, 
and in the fame Time. And if we confider Two other Points of 
the Parabola i ?ci E, viz. % and;-?, we fhall find, that the Ball which 
in the firft Inftant of Time muft have gone to c by the horizontal 
Motion or projeftile Force, is brought down by Gravity to * ; and 
inftead of being carried to d the fecond Inftarit, it is brought to & 
in the Parabola, which Point is dire&ly under and in the lame ho- 
rizontal Line as the End of the 4 th Inch or ■ 2 d Space in the Line of 
FalL£ G. To prove it experimentally ; put on the two Pieces G and 
K of Fig. 4 and 5, then letting the Ball fall from B it will run down 
the Curve B £, arid then in the Air go from b to y, where it will 
make an Impreflion on the Clay : take off the Piece of Fig.$. and 
let the Ball roll down again from B, and it will fall op the Point 

as will alfo be feen by itslmpreflion on the Clay at f, then take 
off the Piece of Fig. 4 . and the Ball will go to E : and laftly, when 
you put on the Board BDE with its Rings r, r, r, the Ball falling 
from B will defcribe the Parabola b E palling thro' all the Rings, ; 
tho' there were as many more, provided the Parabola pafs thro' 
their Centers. N. B, The Reafon why the Bail jailing in 
the Curve B£ acquires a Velocity to carry it forwards uni- 
formly t wice the length or Height B Cj in a Time -equal to the 
Time of the Fall, will be alfo fhewn in explaining the next Law. 

If a Cannon Bailor any other Body be jhot or projected obliquely 
upwards > it will like wife by its Rife, and Fall defcribe a "Para- 
bola. 

Construction. TL 24. Fig. 6. 

Draw a Line A i for the Amplitude of a Parabola, and upon pi, 24 . . Fi 6 
its middle Point 3 raife the Perpendicular 3 E, upon which take the 
Height 3 e for the Axis of the Parabola. From e to E upon the 
Axis continued fet off e E — e 5, and draw the Line A E, which 
will be a Tangent to the intended Parabola in the Point A. Divide 
the Line A E into any Number of equal Parts- as for Example^ 

four, 



2p6 



A Courfe of 




Le£fc. V. four? which will be rftarkM by the Points B V G, D, E: continue 
w*~v~^ on the Line A E beyond F, fo as to fet on upon it four more equal 
Farts as E F, &c. not exprefs'd in this Figure for Want of Rooifr, 
but fuppos'd to be over the Points G, H, I. Then from the Points 
G, D, F, &c. let fall the Perpendiculars Bk f C m y D ^ F s, 
-^Gtij and kftly I/, which will fall upon the Point i of the 
Line A i (or Amplitude of the Parabola.) Divide the Axis e ^ into 
3 6 equal Farts, and mark the Points ^ ^ y 2 , at the End of the 
frrft^, fourth, and ninth ©ivifions j lb that the four unequal Parts. 
■e-q H q x q , and' 23 may relpe&ively contain one, three, five, arid fe- 
ven of the equalParts, Thro 5 the Points cfj and 7, draw the Lines 
dfj.cgf.w<i b h parallel to the Lifie A /, which Lines will meet the 
Perpendiculars in the Points bjA-dxyfogy "and and be Ordinates to 
the Axis e 3. Upon the Line e E or Aiis continued mark e p = eq y 
and <? Z — e z r and likewife e K — e i : from the Points K, Z, and 
p dra w K by Z c, p dj and ori the other fide p fy Z g y and K h. If a 
curve Line be drawn thro r the Fbints A, b i Cy d, <?, g, b v and ij it 
will be a Parabola^ or the Line which a Projectile fliot from the 
Point A in the Direction A B will delcribe y provided it has a Velo- 
city given to it able to carry it the Length A B, in the fame Time 
that by the 'Force of Gravity it would fall the Length B b 9 Pro- 
duce, tOj or beyond t, w\ and f y the Lines/ fj %g y and K h s which 
ijas wSll a&p d y Z r, and K b) are Tangdnts to the Parabola in the 
Poiiits b r Cj d y fy g y By u Then thro' thofe Points draw the Lines 
ba Cy ky dm Y e Oyfqy gs,hu\ and t Xy which will be terminated by 
the Perpendiculars at the Points a y my Cy q y a, and a% and com- 
pleat the Parallelograms AB bay blcky cndm, dp e o y e r f q 9 

f t & s * & w h u -> 1 Xm A a > ^ &i ^ I fy c ntj ft d, d 0j p Cy e q y 
rfyfsy t gy gu, why h ky y i> are all equal; which may be ea- 
fily derhoriftrated from the Conftru&ion, and the Nature of the 
Parabola; but we rather chtife to demonftrate it from Gravity, iii 
the following Explication. 



pi 24. F- 6. Let a Ball be po)t£kt& in the MteMoti ABC DyWc. (JPL 24. 

F. 6.) By the Firft Law it would go thro' the equal Spaces A B, 
B Q GD, DE, EW &c. in eqM Times or Inftants, and go on 
ebntinually in th^ Line A V 7 (Sr. if Gravity did iiot a£t upon it to 
biirig it dovWi ; blit for the Galons before altedged during the firft 
Iiiftaflt> Gravity will have bfought it down i@ b (or, which k the 
famg thing, it will move in the Line A b Diagonal of the Paral- 



Dem o n s t r a r i o m 



lelogram 




W 0] 




lelo^ram A B b a> two contiguous Sides of which B A and A a tepte- Lea. 
fentthe two Forces that act upon the Body Q: and at the End of the 
iecond Inftant, inftead of going forward according to the new pi- 
region A bm the^ineH it will be brotiglit down to r, moving 
in the Line b c Diagonal of the Parallelogram b I c 6, where bl re- 
prefents the now .projeaile !Forcej» and b k -=z B : £. =* ic the Force of 
Gravity, which always prelTing downwards with the fame Force 
muft be reprefented by the equal Perpendiculars A a, b k, c m, d o, 
e q fs, &c j whilft the projeaile Force in its different Direaions 
is reprefented by the unequal and deereafmg Lines A B, A/, en, 
and d p, m the Afcent of the Body ; but in its Defcent, by the un- 
equal increafing Lines cr,ft,g w, and hy ? all Tangents to the 
Parabola. To go on, the projectile Body will fucceflively defcribe 
the Diagonals c d, d e, e f> fg, g h, and h i, of the Parallelograms, 
two contiguous Sides of which reprefent the Quantities and Directi- 
ons of the Forces c //and c m, dp and d o r e r and e q,ft and //, g w 

%ad g u, hy and h x. ' ' t . 

JsI.B. We have caWd ^"Diagonals the Curves intercepted be- 
'tween the > Perpendiculars at the Points A, b, c, d,e,f, &c. 
or which is the fame < thing,inade the 'Diagonals curved f-be- 
caufethofe Diagonals y are realty \<ftch,as >wt ' have ' hinted in 
the Explication oj the Motion of a Body, projected horizon- 




C H O L I V M, 



The Projected Body moves with a Velocity uniformly diminifh'd 
till it comes to the Vertex of the Parabola at e, then goes down 
the other half of it with a Motion uniformly accelerated. For 
fince the Spaces A B, B C, C D^D E, EF, &c. have been taken equal 
in the Line of the firft Direaionof tlie-Projeaile; by the firft Law, 
the Projectile muft go thro' them in equal Times, it none but one 
Force (viz. the projeaile Force) aaed upon the Projeaile. But 
as Gravity aas upon the Body at the fame Time, tho' it cannot 
hinder it from fucceffively reaching the Perpendiculars (which are 
^equidiftant and parallel to each other) in the fame Space of Time 
that it would have done if there had been no Gravity, it will bring 
the Body, at the End of every Tnftant, to other Points of the Per- 
pendiculars, which are ftill nearer and nearer to each other, till the 
Body comes to e : as for Example, the Body at the End of the firft 
Inftant inftead of being at B is brought down by Gravity, to b fall- 
ing one Space equal to e q ; at the End of the fecond Inftant, inftead 



298 J Courfe of Experimental Philofophy. 

Lea. V. of being at C, it is brought down to f, having fallen from the firft 
^~v~w Direction or Line of the projeaile Force thro' a Space equal to e z 
or four times e q — Bi, the Space fallen thro* the firft Inftant • at 
the End of. the third; Inftant, Inftead of being at D, it will He 
brought down to. d thro* a Spaceequal to e 2, containing 9 times 
eq, or B the Space fallen thro' the firft Inftant : at the End of the 
fourth Inftant, inftead of being at E, it will be brought down to 
e, thro' a Space equal to e 3, containing fixteen of the Spaces 
of the firft Fall B f or eq . Now fince the Spaces which the Body 
goes thro' in its Afcent, in equal Times (that is, the Lines A L 
'b c, c d r and d e) are not only lefs than the Spaces A B, BC, C D 
D E, but alfo lefs than each other, becaufe their Change of Di- 
reaion makes them continually cut the parallel Perpendiculars at 
lefs oblique Angles, it is evident that the frojetfed Body continu- 
ally dimintjhes its Velocity till it comes to its utmofi B eight at e 
the Vertex of the Parabok : and this will alfo appear, if we confider 
the Motion of the Projeaile here, as We did that of the horizontal 
Projeaile ; viz, by examining how feveral Parts of the Line de- 
fcrib'd by the Projeaile are like fomany Diagonals defcrib'd by the 
Aaion of two Forces, one of which changes its Quantity and Di- 
rection by extremely fmall Intervals, tho' here we take great Inter- 
vals to make the Thing more plain. 

When therefore the Body projected fetsout at A in the Direaion 
A B, A B reprefents the proje&ile Force, and A a the Fcrce of 
Gravity ; as the Lines B b and b a compleat the Parallelogram by 
tPJ.M-F- 6 -Conftruaion, the Body will go in the Diagonal Kb f. The 
Body being at b will, by the firft Law, endeavour to continue to move 
in die Line b /, being the Diagonal continued, that is in the new 
Direaion which it has now acquir'd, and with the fame Ve- 
locity which it now has (which is lefs than what it had at A be- 
caufe the Diagonal A b is fhorter than the fide AB); therefore £ / 
now reprefents the projeaile Force, and b k the Force or Gravity 
which we take equal to A a ; becaufe we have no Regard to the 
Body's being in Motion, but confider it as fetting out from the 
Point b, by the Aaion of the Two Forces b I and b k ; the Body 
thus aaed upon will move in the Diagonal b c of the com pleated 
Parallelogram b Ic k, with a Velocity as much lefs than it would 
have had in the Line b /, as the Diagonal b c is fhorter than b I. The 
Body at C will, by the firft Law, endeavour to go on in the Line 
c n with the Velocity which it now has, but the Aaion of Gravity 

reprefented 



A Courfe of Experimental Philofophy, Qgg 

reprefcnted by c m (== b k = A a) bringing it down out of that Left. V. 
Line c n will make it go in the Diagonal cd with a Velocity Ieflen'd 
in Proportion as c d is fliorter than cn. Laftly the Body at d a&ed 
Upon by the Forces dp and d o will go in the Diagonal de with 
chang'd Dire&ion and diminiflh'd Velocity, as we have fhewn be- 
fore. 

As the Body comes down from its utmofi Height at it con- 
tinually increafes its Velocity. For, firft, if we confider it when 
at e ; the projectile Force is e r, Gravity e q, and e f (the Diagonal 
of the Parallelogram e rfq) the Line defcrib'd by the Body. Now 
as ,the Line e r reprefenting the Direction and Velocity of the Body 
at e is fhorter than the Tangent f t reprefenting its Direction and 
Velocity when at/ (becaufe e r is perpendicular and ft oblique to 
equidiftant ParaJIels) the Diagonal /£ muft be longer than the Dia- 
gonal e f 9 therefore the Body's Velocity will be fo much the grea- 
ter. Thus will the Diagonal g h of the Parallelogram gwhu, 
the Space gone thro' by the Body in the next Inftant be greater 
thanf g, and confequently its Velocity encreas'd in that Proporti- 
on. And lailly, h i the laft Space being the Diagonal of the Paral- 
lelogram hy ix will be ftill greater than the laft, and confequent- 
ly the Velocity alfo greater. 

COROLLART I. 

Hence may be known the different Velocity of a Projectile in 
any Point of the Parabola which it defcribes, whether in its Afcent 
or Defcent: and it will always be to the Velocity in any other 
"Point „ direclly as the Lengths of the Tarts of the Tangents to the 
'Parabola at thofe Points which ^re intercepted between the fame 
j>r equidiftant Parallels. As for Example, the Velocity at A : is 
to the Velocity at b :: as BC : to b I ; for fince (by Conftrudion) BC 
is equal to A B, and AB reprefents the Velocity of the Body at A, 
as b /reprefents the Velocity of the Body at b ; the Velocities at the 
faid Points A and b will be refpe&ively as B C to b I. Thus if we 
compare the Velocities at A and at d, they will be to one another as 
D E to dp y for the lame Reafon. So likewife in the Defcent the 
fame will hold good ; as for Example, the Velocity at e : is to 
the Velocity at / :: asr 10 : toft ; or er : ft, jo 7 : t 5, or 7 
8 : 56. So the Velocity at/': is to the Velocity at h :: as 5 6 : to 
by; ov ftj or / 5 : to by. 

Q.q. COROL- 



goo A Courfe of Experimental Philofophy, 

Left. V. 

w/ " >r%J COROLLARY II. 

Hence follows alfo, that at equal Heights above the horizontal 
Line or Amplitude A /, the Body will have the fame Velocity ; be- 
caufe it will then be in correfpondent Points of the afcending and 
defending Parabola, where the Tangents, having equal Obliquities 
to the Parallels to the Axis, will have equal Parts cut off by 
thole Parallels wherever they are eqyidiftant. 

CO RO L L A R T IIL 

It alfo follows ; that however unequal the Spaces be that a Pro- 
je&ile defcribes in equal Times, the horizontal Diftances (that is* 
its Advances forwards) will all be equal in equal Times ; but we. 
have already prov'd this another Way. N. B, I don't mean that 
the fame Quantity of froje£lile Force will make a Body go for- 
ward equally faft ; for that will vary according to the Angle 
that its P>ireBion makes with the Horizon ; but that if the Am~ 
plitude of the Tarabola for the whole horizontal Diftance which 
the Body goes thro^ whilft it defcribes any one "Parabola) be di- 
vided into equal Parts by Perpendiculars \ the Body will go. from: 
me Perpendicular to another in the fame Time. 

4. In confidering the Motion of a Projectile^ we have made the; 
Line A i a ftreight Line, which would be ftri&Iy fo if the Earth 
was flat; and indeed fo much of it as a pro jefted Body goes over 
muft be taken for fuch : but if the Force of the Powder, or what- 
ever throws the Body forward, was much greater ; or the Force, of 
Gravity (that is, the Attraction of the Earth) much lefs ; then we 
muft confider the Line A / as a Curve or part of the Earth's Cir- 
cumference* 

* 11.24, F.7. As for Example; Let ABODE* reprefent the Surface of 
the Earth, and AF an high Mountain, fuch as the Veek ofTenne- 
rtf Now if a Cannon was fir'd in the Dire&ion F L, the Ball would 
go forwards. in a Curve, for the Reafbns before alledg ? d, perhaps 
as far as B, where it would come to the Ground. If the Force of 
the Powder was proportionably greater, it would gp as far as G 
before it came to the Ground. Suppofe the Force of the Powder yet 
greater^ and the Ball would go to D ; fuppofe it (till greater, and 

the 



the Ball would go to E, not falling to the Ground till it had gone over Led. VI 

two thirds of the Circumference of the Earth. Laftly, one might rv - A -^ > 

liippofe the Force of the Powder great enough for the Ball not to 

come to the Ground at all, but to come to the Point E from whence 

it fet out at firft, and (the Cannon being remov'd out of the way) 

to go continually round the Earth, at the Diftance of about 3 Miles 

from the Surface of the Earth (that is, at the Height of the Teek 

of Tenner ij) Gravity only keeping it from going off from the Earth 

in a Tangent Line. Were the Force of the Powder greater than in 

the laft Suppofition, the Ball would go farther and farther from 

the Earth in a fpiral Line. 

If the Point F was remov'd fixty times farther from the Center 
of the Earth, or to the Height of 240,000 Miles, that is, to the Di- 
ftance of the Moon; then the Force of Gravity (or the attra&ing 
Force, call'd in that cafe the accelerating Force, of the Earth) 
would be 3600 times weaker than at the Surface of the Earth ; 
becaufe, as we recede from the Center of the Earth, Gravity de- 
creafes as the Squares of the Diftances increafe ; and the Moon being 
-60 times farther from the Center of the Earth, than the Earth's Sur- 
face, the Square of that Diftance 60 is 3600. In fuch a Cafetherd 
would be no Occafion for a greater projeaile Force than that of our 
common Powder to make a Cannon Ball circulate round the Earth, at 
the Diftance of 24000 Miles. The Moon it felf may be confi- 
der'd as fuch a Projeaile ; for having once receiv'd an Impulfe in a 
Line parallel to a Tangent of the Earth, while it is endeavouring 
(by. the Firft Law) to keep its firft (rectineal) Direftion, Gravity- 
is continually impelling it towards the Center of the Earth, and by 
that Impulfe turns it out of the right-lin'd Direction of the projeaile 
Force, and carries it continually round the Earth. Neither can 
Gravity bring the Moon to the Earth, becaufe the projeaile Force 
ftill fubfifting always endeavours to throw off the Moon along the 
Tangent of its Orbit ; and Gravity only alters the Direaion con- 
tinually, whereby the Moon endeavours every Moment to fly off 
along a new Tangent. Thus in every Point of the Orbit, thefe 
two Forces balance each other. 

5. That Endeavour of the Moon, or any other Body that 
moves in a Circle or any other curv'd Orbit, to fly farther 
from the Center of its Motion, is call'd a Centrifugal Force ; 
and the Force ading againft it to keep the moving Body in its 
Orbit (whether it be the Force of Gravity or Attraaion, 

Q.q 2 or 



302 A Courfe of Experimental Phihfophy. 

Left. V. or a String, driving, impelling, or drawing the Body towards 
^V*^ the Center of its Orbit) is call'd a Centripetal Force. Thus when 
a Stone is whirl'd in a Sling, the Stone, which endeavours to (and 
when one of the Strings of the Sling is loos'd, actually does) fly off 
in a Tangent to the Curve which it defcrib'd before, is hindred by 
the Strings to fly off of the Sling from fo doing ; that Endeavour is the 
centrifugal Force ; and the Force of the Strings holding the Stone 
is the centripetal Force. By the Force which endeavours to' 
but cannot really, carry the Stone in the Tangent, the String is 
ftretch'd in a .Dire&ion from the Center of the Revolution -tcfthe 
Circumference. Let us, for Example, fuppofe, that the Body F 
s Pi.^.F. 7 4aften'd to the String M Ff is whirl'd round in the Circle F IN • 
whilft the Body, not held by the String, would have mov'd the 
Length F H in the Direction F G by the firft Law, being retain'd 
by the String it moves in the Arc F I, being brought down from 
H to I ; the Line H I therefore may reprefent the Quantity of the 
Centripetal Force directed towards the Point M ; and the fame Line 
I M dire&ed from the Point M towards H may alfo reprefent the 
centrifugal Force, both, tliofe Forces being equal, otherwife the re- 
volving Body would not be kept in Orbit. For tho' in Orbits that 
are not circular, thefe Forces may encreafe and decreafe (as fhall 
be hereafter fliewn) yet they both equally encreafe and decreafe al- 
ways balancing one another. N. B. The fwifter a Body moves 
zn its Orbit, the more is the String flretched J that is, the greater 
is the Centrifugal and Centripetal Force. If for Example FG 
reprefents the Velocity of the Body infteadofP FL the Booh will 
defer the the Arc F N inftead of F I ; in which cafe the Toint N 
C where the Body is) being farther removed from the Tangent (at G 
where the Body would go to by 'the projectile" Force a lone J the Cen- 
tripetal and Centrifugal Force muft be reprefent ed by the Line 
G N, which is greater than HI. 

All thefe will be further prov'd and illuftrated by the following 
Experiments, & 

Experiment VI. P/. 24. Fig. 8. 

6. ABC D-is a round Table which may be fwiftly tura'd upon 
a Pivot, as at F (the fame that is reprefented by the nth Fia 
JV&V" ? f m { 2 ?*> There is a little Brafs Pipe fcrew'd in at the Center £ 
f/, 3 . 6 ' mto tlie Top of which the String of the leaden Bullet B is thruft fo 
as as to go out at an Hole in the Side of the faid fhort Brafs Pipe ; 

thence 



A(Mtft of E&pe go^ 

thence it Is carried under the Table thro' the Hole \ and fo faftenM Le£l. V. 
tb a Pin in the Side of; tW is laid c/v^O 

at B, if the Table be turn'd fwiftly round, it Mves the Bullet be- 
hind at firft, which thereby appears to have a potion contrary to 
that of the Table, till by the roughnefs of the Surface of the Ta- 
ble, it goes round at laft along with the Table on the fame Part of 
the Table \ then if the Table be flopped on the fudden, the Bullet 
goes on feveral turns,' till haying communicated all its Motion to 
the rough Surface df the Table, it: comes to Reft at laft. - This il- 
luftrates the firft Law of Nature for as the Part of the Table un- 
der the Bullet leaves it behind for a white, becaufe it endeavours to 
cdntinue in its $tk.tie\of';Reft^ for ever leave it where it 

was at firft, if the Table was perfectly fmooth : and when the Bul- 
let is once in Motion it would for ever 20 round on the Tables if 
(befides the Imoothnels of the Table") the String that holds the Ball 
had no FriGion at the Center C. It is alfb to be bbferv'd, that the 
String, which is flack at GB, is always ft retched as at C h by the 
Motion of the Bullet \ arid this fliews the Centrifugal Force. 

If we fcrew a forked Prop toward the f Edge of. the Table f as at 
D, and put the String of the Bullet: into its flit fp as to let the Bul- 
let hang down as at i , the ^orce of the Bullet's: Gravity may be lb 
overcome by the Centrifiugal Force, which the whirling of the Ta- 
ble produces, that the Bullet fhall rife to the' String g d becom- 
ing horizontal : as the Table turns flower and flower, the Ball comes 
down to 0 and fo to 1 1 at laft, r Gravity becoming fenfibje as the 
Centrifugal Force diininiflies; 

Experiment VII. TL 24. Fig. $. 

If a String be tied round the Brim of a Pot full of Water, and Pi. 24 F, 9, 
the Pot be whirPd round, fwiftly about the . Hand or Center K in a 
Circle or Curve of which A C B i^ ari Arc,- the Water acquiring 
a Centrifugal Force /greater than that of Gravity, will not be 
fpilPd when the Mouth of the Pot is downwards. If inftead of 
the Pot, the Glafs W C f {Fig. re.) containing Liquors of different | P1 24 , p. 
fpecifick Gravities be whiPd round the Center K, after they have 10. 
been confounded together by fliaking) they will all recover their 
Places and Tranfparency, even fooner than if the Glals containing 
them had been hung up and at reft. The Reafon is, that as , the 
different Subftances in the Glafs have the fame Velocity given theni 
by the Centrifugal Force, their Momentum will be as their fpeei- 

ficlk 



304 ACmfo 

Le£L V* fick Gravities, that is, their Momentum will be made up of the 
O-v-^ different Quantities of Matter, which they contain under equal 
iL.z.N 0 ^. Bulks multiplied by the common Velocity f which the Centrifugal 
Force gives them in the Line K € from the Center of the Motioii 
towards the C ircumference. Therefore; the' Glafs.Beads.amQngrtK^ 
Liquors weighing more than the Drops of any. of the Liquors* 
will have the greateft Momentum, arid confequently go to the Part 
G molt remote from the Center of Motion K, Then the Drops of 
Oil of Tartar (which is the heavieft of the Liquors contained in 
the Glafs) having for the fame Reafon more Momentum than the 
Drops of the other Liquors (tho* lefs than the Glafs Beads) will 
take up the Space T next to the Beads, and alfo fill their Interftices. 
The next Liquor which is Oil of Peter, will fill up the fpace P. 
And laftly, the Spirit of Wine, whofe props are the lighteft, will 
(notwithstanding its own Centrifugal Force) be brought nearer to the 
Center of Motion and occupy the fpace W ; becaufe the Beads arid 
all the other Liquors having rnore Momentum, drive it from the 
End C, to which it has a Tendency all the while. N. B. The Tube 
is hermetically feaPd at both Ends* 

The Glafs Beads, and different Liquors, fettle in their proper 
Places when the Tube is hung up ; becaufe, as all Bodies tend 
^L.i.N?,B.^ 0Wnwar ^ s with ^ fame Velocity ,* the Momentum 6f Particles 
of equal Bulk muft be as their refpe&ive Quantities of Matter in 
their Defcent : And that the Liquors will not be fo foon fettled 
in this Cafe as when the Tube is whirPd round, is becaufe we can 
give as great a Velocity as we pleafe in the Direction K C, by a 
Centrifugal Force ; whereas that which is owing to Gravity is al- 
ways the fame, 

CO R O L L A R H 

IIence it follows, that a Bottle of any Liquor (which after having 
been muddy is by length of Time become fine, and is again made foul 
by lhaking) may fooner be brought to be fine by a Centrifugal 
Force, than by being fct upright at Reft. 

Ex periment VlIL TL 24, Fig. 1 1 , 

*jpi 24.F. n. JpYK by a String to the two Balls T and M, *• whofe heights 
are to one another as 4 to 2 (here we ule a two-Ounce and a 

four- 



Courje of Experiment at Pfiikjbphy, 305 

four-Ounce-Ball) and pafs the String thro' the oppofite Side-Holes of Left. Vv 
the little Pipe C; let the Length of the String, raeafuring from <-^v~^ 
Center to Center of the Balls, be 18 Inches, and the Pittances of 
the Balls from the Center of the Table be reciprocally as their 
Maflb ; that is, the two-Ounce Ball M mull be at the Diftance of 
i s Inches from C, and the fourO-unce Ball T at 6 Inches from C. 
Let the two little Squares, or rectangular Pieces S s and V v be fix'd 
on the Table at the Diftance of about i Inch or 2 behind the Balls 
to flop them from flying off of the Table, and the long Sides of 
thofe Pieces fo fix'd alternately, that when the Table is made to turn 
in the Direction mark'd by the Dart, the Balls may not be left be- 
hind, but immediately put into Motion. Now let the Table be 
whirPd round with any Velocity, and the Balls will remain at the. 
Points T and M, and defcribe round their common Center of Gra- 
vity unequal Circles * in a reciprocal Proportion of the Maffes,*L. 2. N 0 ;. 
the Momenta given the Bodies by the centrifugal Force being equal, 3 2 - 
and (becaufe of their contrary Direaions) deftroying one another. 
But if either of the Balls be rernov'd farther from C than in the re- 
ciprocal Proportion above-mention'd, that Ball will gradually re- 
cede from the Center of Motion and draw the other along with it, 
till it be ftopp'd by the End of the Piece V v or S s. So the Earth 
and Moon turn round one another and round their common Center 
of Gravity as has been already obferv'd f . + L - * NOi 

Exp e r i m e n t. IX. Pli 24. Fig. 12. 

Let the Table be put into an uniform whirling Motio%-and that 
Motion continu'd (which may be done by a Wheel and Pulley here- 
after to be defcrib'd) and at the fame Time let a Piece of Chalk be 
drawn prefling upon the Table in the right-Line C P, and there 
will by thofe two Motions be defcribed the fpiralLine CDEFP: 
then if the Table be movM again in the fame manner and the fame 
Way (as mark'd by the Dart) and at the fame time the Chalk be 
preft'd ©n the Table in the fame Line P C, but with a contrary 
Direction, viz. from P to C, there will be defcrib'd another Spiral 
like the former, but direded the contrary Way, as is Ihewn by 
the prick'd Line* 



C 0 R 0 & 



god A Courfe of Expmim^d PMoJb^ 

C 0 R 0 L L A R T. 

Hence it follows, that if a Body that has a Centrifugal Force 
whereby it recedes from, or a Centripetal Force, whereW it 
accedes to, the Center of its Motion, at the fame time be car- 
ried round by a Force that gives it a circular Motion; it will fly 
from the Center in a fpiral Line in the firft Cafe, and run to the 
Center in a fpiral Line in the fecond Cafe. 

E x p e r r me n t; X. ■ T/. 2.{ . Fig. 13. 

*pi. 2 |.F. n . On a Piece of Board A E K *,. which has a Piece under it acrofs 
to raife up its broadeft End A E to an Angle of 1 5 or 20 Degrees 
above the horizontal Pofition, are faften'd 3 Tubes AK, CKand 
E K, (but up at both Ends. In the firft there is a fmall Cylinder 
of Cork, which can; eafily Aide up and down the Tube : in the 
Tube CK there is a little Cylinder of Lead moveable in the fame 
Manner : and in the Tube E K, there is an Inch or two of Quick- 
silver fliut up. This Board has a Screw under it, which going 
thro' one of the Holes in the Table (fuch as are mark'd A and B 

-tPl.23 F.i 3 .in ^^ 22. Fig. n)f is faften'd by a Nut fo as to joyri the 
Board of Tubes firmly to the Table. Then when the Cork, 
Lead, and Quickfilver are in that Part of the Tube next to the 
Center of Motion K ; let the Table be whirl'd round, and thofe 
Bodies will after a few Turns be carried to the Ends of the Tubes 
which are fartheft from the Center, tho' 3 01- 4 Inches higher than 
the Ends at K. Put on the Tubes B K and D K, the firft of which 
being filPd with Water has a Cork Cylinder moveable in it ; and 
the other has in it an Inch or two of Oil, the other Part of it be- 
ing full of Water. At firft (when the Table is at Reft) the Cork 
and the Oil will be at B and D the higher Ends of the Tubes and 
fartheft from the Center ; but when the Table is whirl'd round, 
the Cork and the Oil will go towards the Center to K, becaufe the 
greater Centrifugal Force of the Water (being greater than either 
that of the Cork, or that of the Oil) muft give the Cork and the 
Oil a Centripetal Direction, as has been explain'd in the Experi- 

pi. 24. f. 10. naent of the different Liquors in the Glafs of Fig. 10 *. 

7. Monf. Ties Cartes endeavour'd to explain the Motion of the 
Planets round the Sun, by a Vortex or Whirlpool of Celeftial Mat- 
ter 




ter ; fuppofing that the Sun by bjr turning about his Axis, gave Led. V. 
circular Motion to all the Celeftial Matter about it as far as !/V\i 
Saturn and beyond ; and that this Whirlpool of Matter (in French^ 
Tour billon) being without Vacuity (for he afierted "Plenum) carri- 
ed the Planets along with it, and fo was the Caufe of their Mo- 
tion round the Sun. People that did not give themfelves the Trou- 
ble' to examine Things thoroughly, believ'd the Vortices to be the 
Caufe of the Motion of the Planets ; becaufe, where there are 
Whirlpools in Rivers and Brooks, we fee that Straws, little Sticks, 
Saw-duft and other light Bodies are carried round as they float ; and 
therefore it was thought very probable, that the Planets might in 
the fame manner be carried round in the Heavens. But, if we ap- 
ply Experiments and Obfervations to the Dofirine of the Vortices^ 
we fhall find it inefficient for explaining the Motions of the Pla- 
nets. 1 

In the fir ft. place, we'll fuppofe the Planets to be denfer than the 
Matter of the Vortex s and then the fame Thing muft happen to 
them, as happened to the Cork, or the Lead, or the Quickfilver 
contained in the Glafs Tubes, and whirPd round on the Table. 
For the Tubes full of Air being carried round, contained part of a 
Vortex of Air, where the Bodies carried in it were of different fpe- 
cifick Gravities, but all fpecifically heavier than the Parts of the 
Vortex ; and tfiofe Bodies mov'd round and at the fame time agita- 
ted by a centrifugal Force did continually recede from the Center 
of the Vortex, going off from it in a fpiral Line. Planets there- 
fore fpecifically heavier than the Parts of the Vortex would conti- 
nually recede from, the Sun moving off in a fpiral Line. Since this 
won't do, let us fuppofe the Planets all rarer than the Matter of the 
Vortex ; and the Confequence will be-— That as the Parts of the 
Vortex are denfer than the Planets, their centrifugal Force muft give 
the Planets a centripetal Dire£tion, and fo make them go continu- 
ally towards the Sun in a fpiral Line, till they fall into it ; after the 
Manner of the Cork and the Oil in their refpe&ive Tubes of 
Water, where it appeared by the Experiment that the centrifugal 
Force of the Water gave the Cork and Oil a contrary Tendency, 
whereby they continually approached towards the Center in a fpi- 
ral Line. 

There remains only now for the Support of the Carte fian Hy- 
pothefisj to fuppofe that the Planets are of the fame Denfity as the 

R r . Parts 



o 0 g A Courfe of Experimental ThiJofophy. 

Le£t. y. Parts' of the Vortex (and indeed, if there was a Plenum as Monf. 

l^/"Sj 2)^ Cartes fuppofes, all Bodies muft be equally full, and there 
wou'd be no fuch thing as different fpecifick Gravities ; for all Bodies 

pi. 24. F. 2. of the fame Bulk, having the fame Quantity of Matter, wou'd 
weigh equally) and in that Suppofition it will follow that the Planets 
making up Part of the Vortex itfelf will move along with the Parts 
of the Vortex next to them ; and tho' at firft thofe Parts of the 

* Ann. 2. Vortex which are nearefl: to the Sun will move fafteft ; * yet at 
]aft, the whole Vortex will move round like a folid Body or Sphere, 
the Parts moft remote from the Center making their Revolutions 
in the fame Time as thofe which are nearefl: ; which muft be the 
Confequence of a 'Plenum. So that all the Planets wou'd at laft 
have their periodical. Times equal, which is contrary to Obferva- 
tion ; for the periodical Times of the Planets Revolutions are all 
different. Mercury, the nearefl: to the Sun, .performs his Revolu- 
tion almoft 120 times fooner than Saturn, the moft diftant. In a 
word, this is the Proportion of their Diftances and Revolutions, 
viz. The Squares of the periodical Times of the Primary Pla- 
nets round the Sun], and of the Satellites round Jupiter and Sa- 
turn, are as the Cubes of their T)ifiances from their refpeBwe 

fAnn. 2. central Bodies, f 

8. Sin ce then the Cartefian Hypothefls is inefficient for explain- 
ing the Caufe of the Motion or the heavenly Bodies ; we muft 
ihew what is the real Caufe, and that not from Conjectures, but 
from Observations and Experiments. That Gravity or an Attracti- 
on towards the Sun keeps the Planet (or even the Comet) in its 
Orbit about the Sun (and like wife the Satellites about their Prima- 
ries, our Moonalfo being die Satellite of the Earth) whilft the 
projectile Force is continually endeavouring to throw it off along 
the Tangent, will evidently appear from what we have already 
faid, and from Confequenees of the Second Law of Nature, which we 
are going to explain, having firft fhewn feveral Laws relating to 
central Forces by the following Experiments. 

But we muft firft defcribe the Machine for the making tile Ex- 
periments. 

Plate 1 25. Fig. r. 

:pl 25. F. is The Machine for central Forces confifts of a ftrong wooden Frame 
C A B X> H G K E F triangular at Top and Bottom. On the hori- 
zontal 




A Courje of Experimental Phihfophy. c 

zontal Piece G a at Top is a "Wheel G, which (by means of the Left. V. 
String GKHG) when turn'd round, gives circular Motion to the^^y^ 
Pullies and Spindles K L and H I, lb as to move them either with ' r 
equal Velocities, or with Velocities that are as 2 to x , as .3 to 1, 
or as 3 to 2 j becaufe in the Pulley K there are Two Grooves, One 
of 3, and One of 2 Inches Diameter ; and in the Pulley H there are 
alfo Two, One of 6, and One of 3 Inches Diameter. There are 
Two Pieces MN, m n (which we may call Planet-bearing Pieces) 
of about 50 Inches long, to be fcrew'd upon the Pullies K, H, fo as 
to turn round with them. Thefe Pieces have each of them an open 
fquare Tower S, with a little Pulley at Top and Bottom to con- 
duft a String from the Weights S and s, to the Brafs Balls P and/, 
(which we muft here call Planets) fo that when P and p go to- 
wards N or », the Weights are drawn uryf rom their Bafes, which 
is about an Inch above the Bottom of the Towers, and rife within 
the Towers till the Weight-carrying Piece ftrikes the Top of the 
Tower ; each Ball having Two little Wings with Holes in them to 
Aide eafily along Iron Wires that go from one End to the other of 
the Planet-carrying Piece, palling thro' the Two perpendicular Brafs 
Planes M and N, alfo thro' the Towers at about the Diftance of % of 
an Inch from the Surface of the Planet-carrying Piece. N. B. Only 
one of the Wings and one of the Wires is here drawn upon each 
<Piece to avoid Confufion. There are alfo Brafs Collars at H and 
K, in which the Necks of the Spindles (which are of Steel) turn ; 
and iron Screws headed with Brafs at L and I, with little Holes to 
receive the Bottoms of the Spindles. 

The Second Figure * reprefents fomething more than half of one » pi. 25.F. 2, 
of the Planet-bearing Pieces divided into Inches both Ways from the 
Center. B b is the perpendicular Brafs Plane at one End, thro' 
which the horizontal Wires W w, W w pafs, to carry the Planet 
p by its perforated Wings LL, whilft the String that goes thro' 
the middle of the Planet is made faft, by thrufting in the little Pin 
p to give the Planet any certain Diftance from T the Center of its 
Motion before it. is mov'd round by turning the Wheel G (in Fig. 
1 .) S s reprefents the Seclion of the Brafs Tower faften'd to the 
Wood by a crofs Pin, whofe Head is feen at s. T is the Bafe or 
Plate which is to fupport the Weight-carrying Piece, which is re- 
prefented at {Fig. 4,) \ and confifts of a circular Plate and hollow t pi. 2; .F. 4: 
Stem of Two Ounces Weight, and on which may be flipp'd feve- 

R r 2 ral 



g i o A Courfe of Experimental Philofophy, 

Left. V. ral leaden Weights like X Fig.. 5.* At T alfo (^•2,)may be feen 
*-^Y*y the little Pulley under which the String goes. 

*i J l. 25. F. 5. J 00 

t pi. 2 S • f. 3 ." The zd Figure f is a vertical Se£tion of one of the Square Towers 
S \r, with the W eight X and Weight-carrying Piece X x in it, and 
Part of the Planet-bearing Piece, Pulley and Spindle under it, 
marked M N. One little Pulley is faften'd to the Wood at T un- 
der the Plate, on which the Weights ftand ; another is fuftain'd by 
an Iron Arm V S over an Hole S in the Top of the Tower. So 
that the String coming from the Planet P goes firft, under the Pul- 
ley .T, then thro' the hollow Stem of the Weight-carrying Piece, 
and fo thro' the Hole in the Top of the Tower, then over the Pul- 
ley S, fo down again to the Top of the Stem of X where it is 
faften'd. By obferving this Figure, one may eafily fee that if the 
Planet P be mov'd ever fo little in the Direftion P.Q, the Weight 
bearing Piece X will be raifs'd up towards S. 

* ? \*&?\ ^ E W ^ r ^ in § Table which we have already mentioned * for 
24. r 8, ii, ma king feveral Experiments is beft turn'd round by fcrewing on to 
1 2, 1 3/ the Top of either of the Spindles L K or I H, inftead of the Planet- 
bearing Piece MNorw», ' ' 

*pi. 25, f.6. The fixth Figure * reprefents the Seftion of the Wheel and Part 
of the horizontal Piece, the upper Part of the Frame which car- 
ries the Wheel,- and "the upper End of the Piece that fupports it 
mark'd L L L, the Wheel's Axis and fquare- Aiding Collar which 
is moveable on the fquare horizontal Iron H I faften'd to the Wood 
by a Nut and Pin at I, and two Wood-Screws H h. N. B- There 
is a Screw in the fit ding Tiece g to fix the Center of the Wheel^ 
when it is brought forwards or backwards. 

THO\it be of no Confequence of what Bignefs the Machine above 
defcriPd is made, provided its Tarts are proportional; yet for 
the fake of t hofe who would have fuch a Machine made r I give 
here the Meafttres of the principal Tarts of mine in Englifi? 
Inches. 

Tl. 25. Fig. t. 

pi. 25. f. 1. The Thicknefs of the Wood every- where about 1 Inch, except 
the Feet at A and D, where it is 2 Inches thick. 

MN 



MN=^ -='30 Inches* Left. V. 

K H 3 3 l6 Inches. o^v^J 

KL—IH— 8ls Inches, 

AD zr^4L9 Inches. 

A C=C D==2 7 u Inches. 

B C= 24 l8 Inches. 

Diameter of the Groove of the WheelG = 14 Inches. 
Breadth of the Planet-bearing Piece M N or m n = 2 l? Inches. 
Grooves of the Pulley K, the one 2 and the other 3 Inches. 
Grooves of H, the one 6 and the other 3 Inches. 
The Height A K = H D = 1 3 Inches. 

Height of the Towers S or s above the Board MN, mn$i8 In- 
ches. 

Breadth of the Towers = 2 L.3 Inches. 
There ai e 4 

Brafs Planets made ufe of, Two of which weigh 
each • Ounces Troy, and the Two other 4 Ounces Troy each. 

The Weight-carrying-' Plate and Stem weighs 2 Ounces, and 
each leaden Weight (as reprefented by Fig. 5.) weighs 2 Ounces 
alfo. 

What is to be cmfider'd in the Dfe of the Machine. 

The Weights in each Tower are to reprefent the Sun, whofe 
Attra£lion is fhewn by the Force with which the Weight refifts the 
Aftion of the Ball P or p (reprefenting a Planet) that endeavours 
to raife it by the String PTS x f {Fig. 3.) when it receives af PI.25.F.3. 
centrifugal Force by turning the WheelG. So that by putting 
equal or unequal Weights in the Towers by ufing equal or un- 
equal Planets as P, or p ; and by having their Diftances equal or 
unequal in different proportions ; and the Periodical Times equal 
or unequal (as the Wheel-String goes round equal or unequal Pul~ 
lies) we may by Experiments (hew thofe Laws of central Forces, 
which Sir Jfaac Newton has mathematically demonftrated in his 
*Principia. 

In confidering the central Forces of Bodies (for Example, of 
the Primary Planets in refpeft of the Sun, and of the Moons in 
refpe£b to their Primary Planets) which move round other Bodies 
that have an Influence upon them ; we are to obferve Three 
Things. iy?, The Periodical Times, or Times in which the 
Bodies perform their Revolution. idfy\ The Quantity of Matter in 

the 



g i 2 A Courfe of Experimental Phihfophy. 



Led. V. the revolving Bodies. %dly, The Diftance of the Bodies from the 
rs * A -^* v Center of the Revolution. 

Experiment XI. 

First, make the Periodical Times equal, by putting the Wheel 
String into the 1 Inch Groove of each Pulley, croffing it before each 
Pulley to give it the more Force to move the Pullies, but fo that 
theTullies may both turn the fame Way that the Planet-bearing 
Pieces may not unfcrew. Then put only the Weight-carrying 
Piece in each Tower: and laftly, fatten to their Strings a 2 Ounce 
t pL 2 s- F - 1 ■ Brafs Ball, as P and p, -\ at the Diftance of 1 2 Inches from the Cen- 
ter on each Planet-bearing; Piece. So you will have the Periodi- 
cal Times, the Quantities of Matter j and Ui fiances from the 
Center equal. Give circular Motion to the Wheel G, and the 
Planets by their centrifugal Force will raife the Weights S and s 
at the very fame Inftant of Time ; which fhews, that in this Cafe 
the centrifugal ^Forces are equal. N. B. If upon each Weight- 
carrying apiece you put on one or two, or more equal TV eights (fuch 
as are exprefs'd by Fig. 5.) the Tlanets will always raife them 
at the fame Inftant, provided the Wheel be turned proportionally 
f after as there is more Weight. 

Experiment XII. 

Secondly, Inftead of / put on a 4 Ounce Ball, and double the 
Weight in the Tower j- q ; then turn the Wheel, and both Weights 
will rife at once. This fhews, that when the Quantities of Mat- 
ter in Tlanets are. unequal, but the Tiiftances and Periodical 
Times ft ill remain equal, the centrifugal Force is proportional 
to the Quantity of Matter. 

E x PERI M E n t XIII. 

Thirdly, Take off the 4 Ounce Ball, and make ufe of p again, 
but put it only at 6 Inches from the Center. Take the additional 
Weight from s and add it to S ; that is, let the Weight S, which 
has P at 12 Inches Diftance, be = 4 Ounces ; and the Weight /, 
which has p but at 6 Inches Diftance, be = 2 Ounces : then upon 
turning the Wheel, they will both rife at the fame Time, fjence 
it is plain, that if the F 'eriodicai '■ Times, and the ' Quantities of 

Matter 



A Courfe of Experimental Phihjbphy. 913 

Matter continue the fame, but the ^Dif ances are different j thehed;. V. 
ceMrifugal Forces willbe as the 'Diftances. h^QQ^ 

Experiment XIV* 

Fourthly, at the Diftance of 6 Inches, where p was laft, 
change / for a 4 Ounce Ball, and put equal Weights in the Two 
Towers ; then when you turn the Wheel, both Weights will rife at 
once *, which fhews, that when the "Periodical Times are equal j 
and the Difances from the Center reciprocally as the Quantities 
of Matter in the TlanetSj the Centrifugal Forces are equaL 

Experiment XV. 

Lastly, Change the String on the Pulley H, putting it into the 
Groove of 6 Inches Diameter, fo that the Periodical Time of the 
Planet p may be double that- of the Flanet P, which laft will then 
move twice as faft, if its Diftance be the fame- from the Center, 
which it muft be in this Experiment. Put 8 Ounces in the Tower 
SQ, and only 2 in the Tower s q y the equal Planets P and / be- 
ing then each at 1 2 Inches Diftance from the Center. Turn the 
Wheel, and both Weights will rife at once. This fhews, That 
planets, that have >an equal Quantity of ^ Matt er and the * fame Dif- 
tance from the Center, but different Ter iodic al Times, have their 
centrifugal Forces reciprocally as the Square of their Ter iodic al 
Times \ tlrat is, direBly as the Square of their Velocities. 

COROLLART. 

Hence follows, that if the fame Planet changes in Velocity in 
the fame Orbit, its centrifugal Force will encreafe or decreafe ac~ 
cording to the Square of the Velocity which the Planet has in that 
Part of its Orbit. 

S C 1 H 0 L I V M 

When we compare the laft Experiment with the 1 5th Experi- 
ment, and find that the Planet (/? going round in a Circle of 12 In- 
ches Radius at the fame Time that P went round in a Circle of 6 
Inches Radius,) raisM twice the Weight becaufe it had twice the 
Velocity j it will appear ftrange, that in the laft Experiment^ where 

/(going 



3 1 4 A Courfe of Experimental Phihfophy. 

Left. V. f (going twice thro 7 a Circle of 12 Inches Radius, whilft P goes 
o"W once thro' fuch a Circle) has but double the Velocity of P, it fhould 
now^raife four times more Weight. But this Proportion (which 
is of very great ufe in explaining the Motions of the heavenly Bo- 
dies) will be very clearly deduc'd from a Confideration of the Firft 
Law and what we have faid upon it. 

+H.z4,F. 7 . Round the Body fuppofed at Mf CP late- 24. Pig. 7.) or the 
Center M, let a Planet revolve in the Circle FIN; it is plain, that 
when it defcribes the Arc FI, its centrifugal Force is reprefented 
by the Line HI: then if the fame Planet be fuppofed to defcribe 
the Circle finoi double the Radius, in the fame time, it is evi- 
dent that it will have a double Velocity, and confequently will de- 
fcribe the Arc / n in this Circle in the fame Time that it defcribed 
F I in the little Circle ; fo that now g », which is double of H I or 
h i (becaufe the Triangles f g M and F H M as well as the Arcs fn 
and F I are fimilar) will reprefent the centrifugal Force to be dou- 
ble of what it was in the little Circle. But it, inftead of going in 
the great Circle, the Planet doubles its Velocity by going twice 
round the Circle F I N in the fame Time that it went once round 
before, it will defcribe the Arc F N, of twice the Number of De- 
grees, inftead of F I ; and as the Arc F N (tho' of the fame Length) 
is twice more curve than f n,^ the Planet atN will recede from the 
Tangent twice as much as if it was at >/, confequently four times 
as much as when at I with half the Velocity. Therefore the cen- 
trifugal Force at N : will be to the centrifugal Force 'at. I:: as 
G N : to H I ; or as 4 : to i . 

N. B. This holds good only in fmall Arcs, as VI and F N are 
fupps'd ; but then it is only to be confided d in fuch. 

There are many more Experiments relating to central Forces 
to be made with this Machine; but thefe are fufficient for our pre- 
fent Purpofe. However, for the fake of the Curious we flhall men- 
t Ann. 3. t j on a f ew more in the Notes, f 



LAW E 



A Courfe of Experimental PUlofophj 



The Second Law of Motion. 

ic. The Change of Motion is always proportionable to the mo- 
ving Force imprejfed ; and is made in the right Line iii 
which that Force is irnprefs^d. 

If any Force generates a Motion, a double Force will generate 
double the Motion, a triple Force triple the Motion, &c. whether 
that Force be imprefs'd all together and at once, or gradually and 
fucceffively. And this Motion (being always dire&ed the fame 
way with the generating Force) if the Body mov'd before, is added 
to or fiibtra£ted from the former Motion, according as they di- 
rectly confpire with, or are dire&ly contrary r to each other ; or ob- 
liquely joyn'd when they are oblique, fo as to produce a new Mo- 
tion compounded form the Determination of both. 

i i. Let the Body A * receive an Impulfe in the Dirjeftipn A L, 
fo as to go thro' any determinate Space in a determinate Time; as 
for Example, the Space A B or one Rod (r6 i Feet) in a Sgopjid 
Minute of Time. The^ody will, according to the firft L#w, by 
Virtue of the Force imprefs'd, go on unifbrniity thr^ the Spaces 
AB, BC, CD,DE 9 EF, FG, GH, HI r IK, KL, fe,foas^ 
fcribe each of them (fuppofing them all equal) in a Second, and fp 
on in infinitum. Now when the Body is in Motion, If the fame 
Force that afted upon it at firft, or one equal to it, fhould aft up- 
on it again in the lame Dipe&An, when it is at f B for Example ; 
then would the Body be carried thro' a dawdle Space, viz. (tjbe 
Space B D, in a fecond, and fb thro ■ D F, F H, iHK, Mc. jbievery 
Second, that is, with double Velocity ; beeaufe, whilft it .was going 
on at the Rate of one Rod in a Second, it jreceivM an Addition of 
Force capable of making it go alio a Rod in a Second, and cpafe- 
quently that Addition of thofe two Forces ithat. conlpire. give the 
Body a double Velocity. If the Body in Motion, .. when M B % 
had received the Second Impulfe by a Force double of the ikft 
Force, it would after that Impulfe go on in each -Second thro' the 
Spaces ME, EH, HL,&r. that is, with a triple Velocity. If af- 
ter receiving the Second Impulfe with a Force equal to ^the firft, 
while it is going on with double Velocity (for Example, thro' the 
Space B D or D F, &c. in a Second) it fhould receive a third Im- 

S f pulfe 



.1 



1 8 A Courfiof- Experiment a 




pi 



Lech V. pulfe (ftill In the fame Direction) equal to the firft, then it would go 
from D to.G, and fo on from G to K, every Second of Time^ 
F * 7 ' that is, with a triple Velocity, after three equal Impulfes, juft as it 
would do after two unequal Impulfes in the Proportion already ex- 
plained : as it would alio do if it had received but one ImpuHeat 
firft, but three times greater than we then fuppos'dL 

12. If, whilft the Body by the Force imprefs'd is (by the firft 
Law) going on uniformly thro 5 the Spaces' A B, B C, &c a Force 
equal to the Force imprefs'd fhould a£t upon it in the Direction 
L A (that is, in a contrary Direction) the Body would lofe all its 
Motion- But if this laft Force fliould only afl: upon it after it had 
received feveral Impulfes according to the firft Direction, it would 
only deftroy fo much of the Motion as its own Quantity of Force 
would be capable of producing : for Example, if the Body, after 
three Impulfes, was going on thro' the Spaces D G, GK, &c. that 
is, 3 Rods in a Second, and then it fliould receive a fourth Impulfe, 
but in the contrary DireQion, it would only lofe fo much Motion 
as to go thro 9 but two Rods in a Second, and continue to go on 
uniformly with that Velocity, juft as if it had received but two Im- 
pulfes. Again, if when it is going 3 Rods in a Second it fliould re- 
ceive two Impulfes at once eqtial to the fir% but in contrary Direfti- 
ons, one in the former and the other in the oppofite Dire&ion ; thofe 
Forces would deftroy each other, and the Body would go on uni- 
formly with the fame Velocity that it had before thofe Impulfes^ 
viz. 3 Rods in a ..Second 

13. Now, let us once more fuppofe the Body to be going on uni- 
formly at the Rate of a Rod in a Second or thro' the Spaces A B; B C, 
Cjr. Suppofe when it is a£ E, a new Force equal to the firffi 
(or equal to the Force which the Body has then) fliould a£t upon- 
it in the Direction E or at right x Angles to its prefent Direftion 
AL; the Body would change its Direction, and move (as has been- 
fhewn) in the Diagonal Ef of the compleated Parallelogram E ef 

t l. 3- N*. p # ^ If the new Force had been double, then the Body would have 
Jo L 3 * 5 ' gone in the Diagonal Ef of the double Parallelogram E e f F. But 
if the new Force had been only equal to half of the firft Force 
imprefs'd, then the Body would only have gone in the Diagonal 
E $ of the Parallelogram B -1 <p F*. 



GOROL 



d Courfe of Experimental Philofophy. 319 



Le£t V. 

C O R O L L A R T h 

Hence it follows, that let the Quantity of the new Force be PL 2 *- F - 7- 
what it will, if it ads at right Angles, the Velocity will be grea- 
ter than if the Body had continued in its firft re&ilineal Directi- 
on ■ ; becaufe (as' has been fhewn t) the Body by the A&ion of the t l. a°; 
two Forces defcribes the Diagonal in the fame Time as it would g 6 a ^ Pa s c 
have defcribed either Side of the Parallelogram by the fingle A&i- 
on of one of the Forces ; and in the Parallelograms E <p, Ef E f, 
the Diagonals are longer than the Sides, as they fubtend the 
right (that is, the biggeft Angles) of the rectangular Triangles 
E F <r> EF /, and E F f. * N. B. When we make ufe of thefe * By i 9 . i. 
Words the Force impreffed^ or the innate Force, we mean the EuQl 
Force which the Body has when it is in Motion, without con- 
fidering what fir ft gave the Motion : That is^ we mean the fame 
thing that Sir Ifaac Newton calls Vis infita. 



C O R O L LA R T II. 

Hence follows alfo, that if the new Force a£ts at acute Angles, 
its EfFe£t will be more confiderable the acuter the Angle is; but it 
will never encreafe the Velocity of the Body fo much as if it a£ted 
at no Angle, that is in the fame Direction. For Example, fuppo- 
fing the new Force equal to the Force imfrefifd, and its Direction 
to be in the Line F g, G F gwill be the acute Angle made by the 
two Directions. Now it is evident, that the lefs the Angle G F g 
is, the greater will be the Angle F G and confequently the Dia- 
gonal Fg (expreffive of the Body's Velocity) which fubtends that 
Jungle will alfo be greater : but whilft there is any acute Angle 
at F, there will be an obtufe Angle at G, and G Fg will be a Triangle 
in which one fide F g will always be lefs than the Two other Sides 
F G and G#,t which are equal to the Two F G and GH thro'f By 20. 1, 
which the Body goes, when the Two Forces a£l in the fame Di- EucL 
. region, in the fame Time. 

C 0 R O L L A R T lit 

It follows like wife, that the new Force may a£fc upon the Body 
in fuch a Direction, that the Body will not be accelerated thereby ; 
nay fome times retarded. For if the new Force neither confpires 

S f 2 with 



Led. V. with the Force impreffed, by atHng at acute Angles with its Di- 
v^yt^ re&ions, nor a£ts"at right Angles with it ; the Body may keep its 
ti. 2.5. r. .7. yoi oc [ t y t ho' in a new DirecHon, nay even go flower when the 
new Force acts at ofotufe Angles. Let u% for Example, fuppofe 
the new Force^ equal to the Force imprefs'd, to a& when the Body 
in 'M o'tio'n is at K, in the Direction K k, fo that the ofotufe Angle 
LKk may be of 120 Degrees : then will the Diagonal K 1 of the 
Parallelogram K k l L be equal to the Side K.L, foecaufe KL 1 and 
K k 1 areltwo equilateral Triangles, and therefore the Body w ill 
liave the fame Velocity as before. But if (every thing elfe remain- 
ing as We have 'fuppos'd) the new Force fhould be lefs than the 
Force imprefs'cl, as for Example, only equal to half of it, the Ve- 
locity of the Body would be climinifh'd : for then K k would re- 
prefent the new Force and K I Would foe the Diagonal of the Pa- 
rallelogram (which Would how beKL Ik f) and K l falling from 
•K one Angle of an equilateral Triangle upon the Middle of its 
oppofite Side would be fhorter than any of the Sides ; therefore, 
&c. If the new Force was more or lefs than half in any Propor- 
tion, the Velocity of the Body would indeed be leffen'd, but not 
fo much ; for then the Point / would fall between L/, or between 
/ I, and in any of thofe Cafes the Diagonal would be longer than 
X / becaufe K / is perpendicular to L 1, and the faid Diagonal would 
foe ohliqueto it, therefore longer, tho' ftill ffoorter than the Side K L. 

If the new Force had been greater than the Force imprefled, 
for Example double, the Body then (fujipofihg the Angle of &p- 
'.plication the ; #fne) : WotfId''6ftCreafe:its Velocity by^ the Action of 
it, for the new^orce being reprelented by K 1 , the Diagonal or Velo- 
city would be' KV longer than K L. But then if the Direction of 
this greater Force fhould be more oppofite to the Direction of the 
jForce imprefs'd, that is, if the Atfgle LK 1 fliould be encreafed, 
:for Example 30 Degrees more, fo as to become L K ?, then the 
Body would hot change its Velocity with its new Direction, be- 
caufe it ' wou'd go in the Diagonal K k, which is equal to K L. 
Nay, if ' the Angle of Application fhould be greater than K L 3, or 
of more than 1 50 Degrees, the V elocity of the Body would be di- 
minifh'd, the new Diagonal becoming fhorter than K k. 

If the new Force was only equal to the Force imprefs'd and its 
Direction K 4, that is, if the Angle of Application fhonid foe of 1 50 
Degrees, the Velocity of the Body would be diminilh'd by half, 
*fe»gonal K5 being then but the half of K 1 (= K L) becaufe 



A Courfe of Experimental Philofophy. g 2 1 

it fubtends the Angle K L 5, which is but half of the Angle & L L Left. V. 
N. B. Knowing the Angle of Application and Quantity pf the kS*Y\J 
new Force,, we may^ always know what will be the Velocity of the li ' 25 ' Fe 7 ° 
Mody after the ABion of the new Force becanfe the Ttiagonal 
that Jhews it, is always known ; as it is one Side of 0 Triangle , 
in which Two Sides reprefenting the two Forces 4?$ gi?J.en, and 
the Angle betweem them.j a&d cmfequemtly the gd Mde. 9 f which isi %y i s- an <* 
the faid Diagonal The Angle known does alm&ys mntain the 17 ' 1 EuclkL 
Number of *D$gmes that the Angle of Application wmts. of 
i So. Thus in the Trkmgle K h ,L;, where K L and L k (== K 2) 
reprefent the /Forces s (jmmfe of the ^Parallels K % md L k) 
* the Angle Khkis eqml : to IK which .3L K % wants of . :1 $ c * By 29. x f ' 
degrees; 'and cmfeyueu&fy the DiqgtmS Ktk, which fidtends 
Angle, is known. . 

ci 4 • It has h@m ©bferv'd ^hat when a Eoiy falls during one Se- 
cond of Timt, it goes thro' a Space equal to 16 j Englifh Feet, or 
one Rod, as we have already mentioned : # ^ therefore the Ftorce im- 
prefled by Gravity at the Beginning of its Ball is capable of making 
the Body .go downwards at the Rate of one Rod in a Second, ~-\ tho' t By the- firft 
it-lhoula:.a£b no longer upon it than during the firft Second ; that ^86 ? 2 8- ge 
is, tho'tfhe Body fhould for ever after ceafe to be h#avy. For ex- ' 7 
ample, if the Body A * falls thro 7 the Space A B during the firft* pl - 2 5' F - 8 < 
Second of ; its Fall ; if then it fhould ceafe to b^heavy^ yet it would 
;go thro 5 the Spaces equal to A B during all the Succeeding Seconds 
of Time, viz. thro' the Spaces B r ;D, D <?, e f /G, G v£, h /, 
iky k L ? &c. But as the Body does not ceafe to be heavy, we muft 
confider the A£tion of Gravity as an Impulfe given by a new Force 
equal to the firft, a£ting downwards when the Body is got to B 
at the Beginning of the id Second, and the Body during the 2d 
Second will go thro' the Space B D double the Space AB, or equal 
to the Two Spaces B c and c D. Then if the .Body fhould ceafe 
to be heavy, it would go uniformly thro 9 the double Spaces D /, 
f h y &c. every Second ; but Gravity a&ing upon it alfoat the Be- 
ginning of the 2d Second, when it is at D, Superadds a Force able 
to make it go thro' a Space equal to the -firft A B in a Second : 
confequently it will go thro' 3 Spaces or Rods (or thro' a Space 
D G equal to 3 Rods) the 2d Second. At the Beginning of the 
fourth Second, Gravity a&ing by a fourth Impulfe fuperadds a 
Force equal to the former, whereby it will ;go the Length ,X3L, 

that 

** Bodies imredity only fall \b Englijh Feet -and one forth of a Foot in a Second; hut <we call that 
Space here 1 6 and aha If Feet ; becaufeoue Rod ( which is aMeafure of 16 and a half Feet ) gives us 
fuch a Number as to avoid Fractions in the Examples of the Calculations that vue give. 



322 A Cmrfi of Experimental Philofophy. 



Left. V. that is, four Rods or Spaces the fourth Second : and fo on ; f and 
l/~V~\-; this will be a Motion uniformly accelerated. 

This Motion of a Body thus accelerated in its Defcent would be 
the real Motion of falling Bodies, if Gravity afted by Intervals, 
as we have only fuppos'd, it helps Conception: But as Gravity ne- 
ver ceafes to act, we muft fill up the Intervals between the Begin- 
ning and End of every Second or fmall Part of Time, 
* PL 25.F.9. Thus ? if we confider the Body falling thro' the Space A B * (Fig 9.) 

in the firft Second, we muft not only confider Gravity fuperadding 
a Force capable of making the Body fall one Rod farther at the 
Beginning of every Second • but alfo during the Time of every Se- 
cond. For Example, at B at the Beginning of the 2d Second, the 
Body not only receives an additional Impulfe to carry it to d in-, 
ftead of r, but alfo during the Time of the 2d Second another Im- 
pulfe which makes it go to E inftead of d ; fo that the Body will 
fall 3 Rods during the 2d Second. Likewife at the Beginning of 
the 5 d Second when the Body is at E, it will again receive from 
Gravity one Impulfe at the Beginning of that Second, and another 
during the Time of it ; fo that it will go thro' the Five Spaces E /, 
fgy Z h i and i K during the Time of that 3d Second. So in 
the Time of the 4 th Second the Body will (for the fame Reafon) 
go thro' feven Spaces or Rods from K to R, and fo on, the Number 
of Spaces defcrib'd encreafing by two every Second ; that is, ac- 
cording to the Series of the odd Numbers 1, 2, 5, 7, 9, &c. 

This is the true Manner of Bodies falling with an accelerated Mo- 
tion by the Force of Gravity, abftra£Kng from the Refiftance of 
Air, which we fhall hereafter take into Consideration. N. B. All 
Bodies fall equally fwift where there is no Air, as has been 
proved by the Experiment of a Tiece of Gold and a Feather fall- 
ing in the fame Time from the fame Height in an exhaufled Re- 

15. What we have flhewn (Step by Step) of the Effect of 
Gravity on falling Bodies, may be demonftrated another way af- 
ter Galileo's Method, thus. As Bodies (abftrafting from the Air's 
Refiftance, as we have faid) encreafe their Velocity in falling ac- 
cording to the Time during which they fall, Galileo reprefents 
the Times and Velocities by equal right Lines, which he joyns at 
right Angles ; and then joyning their other Ends by a third right 
Line, makes a redangnlar Triangle of which this laft Line is the 

Hypotenufe 



A Courfe of Experimental Philofophy: 5 2 



Hypotenufe to reprefent the Space fallen thro' in a certain Time ; Left. V. 
A B, for Example, -j- reprefents the Time ; B V reprefents the Ve- .^-^V^J 
locity ; and the Triangle A B V the Space gone thro' during that ) 0 _ L 2 ^ t - 
Time ; as for Example, one Rod, if the Time be one Second. 
Now if the Time be double, A C reprefents it ; and then the Ve- 
locity being double alfo, the Line C U mult reprefent it. Draw 
U A,and the large Triangle AUG will reprefent the Space fallen thro" 
in that Time; which greater Space being divided into Triangles 
equal to the Firft A B V, will appear to contain four of them. 
Therefore, fince a Body falling one Second of Time goes thro' the 
Space of one liod, the fame Body falling two Seconds will go thro 7 
the Space of four Rods. Had the Time been AD (= 3 Seconds) 1 
the Velocity wou'd have been D v =AD, and the Space A v D* 
9 Rods, or 9 of the Firft Space. Thus if the Time be A E = 
4 Seconds, the Velocity muft be E u quadruple of B V, and ths 
whole Space A u E containing 16 times the Firft Space A V B. 



C O R O L L A RT I. 



Hence it follows,, that if you multiply the Times by the Veloc> 
ties, or if you fquare the Times, or fquare the Velocities, you- 
will have the Number of Spaces (equal to the Firft) which the Body 
has defcrib'd during its whole Fall. As here, the Times being 4, 
and the Velocities 4, the Spaces gone thro' are i6~ 

C 0 R 0 L L A RT XL 

Hence follows alfo, that if you mark the Times (or Number 
of Seconds) as the Numbers, 1, 2, 3, 4, in the Scheme fhew ; you 
will have, againft any of the particular Numbers, as many little Tri- 
angles as the Body has gone thro 1 Spaces during the Part of Time ex- 
prefs'd by that Number. For Example, there is on the left Hand 
One Triangle over againft the Number 1, Three over againft 2, 
Five over againft and Seven over againft 4. And to know how 
many Rods a Body falls in any determinate Second or Part of 
Time, as for Example, in the icth Second, without drawing the 
Scheme ; we muft firft find how many Rods the Body falls in the 
whole Time, as here in 10 Seconds ; then how many Rods the Bo- 
dy falls in 9 Seconds, and fubtracT: the laffr from the firft. to X 10 
is ioc the Number of Spaces in 10 Seconds : 9 X 9 is 81 the Num- 
ber of Spaces in 9 Seconds ; 81 from 100 leaves .1 9,, the Spaces or 
Rods fallen thro' m the 10th Second* 



324 A Courfe of Experimental Philofophy, 

Le£t. V. 

C/ " v ^ COROLL^RTIIL 

It appears likewife, as a Confequence from what has been faid, 
that when a Body has fallen thro' a certain Space by a Motion uni- 
formly accelerated', it has acquired fuch a Velocity as is able to car- 
ry it thro ? a double Space in the fame Time, if Gravity fhould 
ceafe to a£fcj or have its Effe£t any way deftroy'd, or if the Body's 
Dire&ion fliould be changM from a vertical to an horizontal one. For 
+ pi. 25. F. Example, when the Body in the Time A B f, falling thro 5 a Space 
IO - reprefented by the Triangle A V B, has acquired the Velocity B V ; 

if, Gravity ceafing to a£t, it receives no Addition to its Velocity, 
tho' it continues to fall during the TimeB C — A C, fo that the 
whole Time muft be reprefented by the whole Line A C ; yet the 
Velocity will not be reprefented by the equal Line C U, but by 
the Line C k equal to B V the Velocity the Body had when it 
ceas'd to accelerate its Motion ; therefore to know how many Spa- 
ces the Body has gone thro' in the TimeB C .= A C with an uni- 
form Motion, we mull multiply B C by CJr = B V the unchanged 
Velocity of the Body, and we fhall have the Re£kngle B V*C K con- 
taining two Triangles equal each to A V B : that is, two Spaces willbe 
run thro' by the Body moving with an equal Motion in the Time B G 
equal to the Time A B in which the Body defcrib'd only one Space 
by an accelerated Motion. So likewife, if the Body having fallen thro 1 
4 Spaces during the Time A C,and having at the End of that Time ac- 
quired the Velocity C U ; the Velocity be no more encreas'd and 
the Body continues to fall during the Time C E=A C, it will fall 
thro' Siipaees inftead of 12 that it wou'd have fallen if the Velocity 
had continued to encreafe fo as to become E~u at the End 6f the Time 
C E ; but as it is then only E : e, equal to V C its Velocity at the 
Beginning of the Time C E, we muft multiply C E the Time by 
tJ G or E e the uniform Velocity, and then we ihall only have the 
ReCtangle V C E e containing 8 Spaces inftead of the Trapezium 
C U uE r containing 1 2 . 

This will becortie vifible by changing the Dke£tion of the mo- 
vihg Body from a vertical to an horizontal one, for Gravity a&ing 
only perpendicularly will neither accelerate nor retard the Body rin 
its horizontal Motion. N B. Th&mmmr^ -of. doing this we Jhall 
her&dfHrjhew* 

i6Tf 




Led. V. 

CO ROLL ART. IV. unPu 

We may alfo further gather from what has been faid, that Gra- 
vity does not aft by Intervals^ (tho 7 we explained it that way at firft 
to facilitate Conception) for if it did, after every Impulfe the Body 
a£ted upon wouM go on with an uniform Velocity, tho ? it would 
have a greater Velocity after every Impulfe. Neither after it had 
fallen a certain Space would it have acquirM a Velocity capable of 
carrying it thro* double that Space in the fame Ti&ie, fhould Gravi- 
ty ceale to a£t, but only thro' a Space equal to the firft. 

For Example ; after GaliUo's Method, the Triangle A C B?L*s. F. u. 
(TL k. Fig. \ i.) reprefents the Space fallen thro 5 in any Part of 
Time, fuppofe one Second, in the Time A B with a Velocity naf- 
cen t (or juft beginning) at A the Beginning of the Second, and equal 
to C B at the End of the Second : whereas if a Body fhould fall 
one Rod in a Second by an Impulfe as a Blow, the Velocity at firft 
would be equal to A D and continue fo during the whole Time, lb 
that at the End of the Second it would only be B V equal to AD 
and half of B C, whereby without a frelh Impulfe it would only 
carry the Body down one Rod more in another Second ; for then 
the Time ^multiplied into the Velocity would only produce the Rec- 
tangle AD VB equal to the Triangle ACB ? becaufe it is of the 
fame Height and has half its Bale, f tBy ^i. u 

Euclid. 

r 6. If the Dire£Hon of a falling Body be fo changM as to make 
it go diredtly upwards beginning that Motion with all the Veloci- 
ty it had at the End of its Fall, it will go up (by a Motion uni- 
formly retarded) exa&Iy to an Height equal to that from which 
it fell ^ and the Spaces it goes thro 0 in each Part of the Time are to 
be feen in the Scheme over-againft the Numbers reprefenting thofe 
Parts of Time. If, for Example, the Body has fallen 4 Seconds, it 
will have gone thro' 16 Rods in its Fall, and have acquired the Ve- 
locity Eu f capable of carrying it 2,7 Rods in the fame Time by an+ pi. 25. f. 
uniform Motion; but as Gravity a£ts againft it in its Rife it will IO - 
deftroy all its Motion by the Time that it has rifen only 16 Rods ; 
for it is the fame thing to make a Body from Reft move 16 Rods 
downwards in a certain Time, as to deftroy half of the Force which 
was able to carry a Body upwards u Rods in the fame Time. 
The fame Thing will alfo be plain if you confider the whole Time, 

T t as 



326 A ' Cowje of Experimental PMhjbphy. 

Left. V. as divided into fmall Parts, and obferve the uniform Diminution of 
^ry^ the Body's Motion, For Example ; let the Body be thrown up- 

pi. 25. f. 10. wan j Sj an( j j et t fc Q spaces which it goes thro' in every Second be con- 
Rder'd. If the Velocity given to the Body proje£ted upwards be 
fuch, that in the Time E D (which will now be the firft Second of 
Time) it goes thro' 7 Rods* the next Second it will go but % be- 
caufe Gravity gives it an Impulfe downwards at the Beginnirig of, 
and during, the id Second, able to carry it downwards 2 Spaces or 
Rods; which is (in other Words) to take away 2 of the 7 Spaces, 
which the Body would have gone thro' in that Time. Thus like- 
wife, inftead of going 5 Spaces the 3 d Second*, Gravity taking away 
2, it will go but 3 Spaces ; and the 4th Second (the laft of its Rife) 
inftead of going 3 Spaces, it will for the fame Reafon go but one ; 
and then the Body will for an indivifible Moment of Time be at 
Reft. From the Point of Reft the Body will come down again, 
falling with an accelerated Motion already defcrib'd, and coming 
down juft in the fame Space of Time that it Went up, 

S C H O L IV M. Tl 25 . Fig. 12. 

PL 25.F, 12, If a Body , inftead of going upwards in the Line A B> Ihould rile 
to the lame Height in the inclined ftreight Lines A C or A E, or 
in the Curves A a G or A e E, it would in the larfte Time confte 
down in the ftreight Lines G D orEF, or in the Curves C^ D or 
E/F. For we have already fhewn, that when a Body is a£ted up- 
on by a Force to carry it in the Line A B in a certain time, if an- 
other Force A g a£ts upon it too, the Body will go in the Diago- 
nal A C of the Parallelogram A B Cg in the lame Tirtie : And we 
have alfo fhewn, that it would go in a Parabolic Curve A e G in thfe 
fame Time from A to G. Now fince the Force of Gravity in the 
Direftion B A, which deftroys the Motion of the fifing Body, is 
equal to the Force of Gravity a<5Hng in the Dire£tion Qg to make 
the Body fall from its Point of Reft C, the Forces C E and G g 
are equal to Ag and A B, and therefore the Diagonal right Line 
C D, or curv'd Line C c D, will be gone thro' in the fame Time as 
the Lines AC and AaC, The fame might be faid of the Lines 
A £ and A e E compar'd with EF and *Le F. N. B. When we 
throw a Body dire El ly upwards and it falls upon the fame Tlace 
of the Earth we threw it from ^ then it really defcribes Two fuch 
Lines as A C and>C.l± ( inoving;fromA ioT> by the Motion which 
the Earth gives it from Ea$ to Wefl. But if we Jhoot it o&~ 

liquely 



A Courfe of Experimental Thilofopl j. 227 

Uquely upwards it defer ibes the two Curves A C, C D,or the Ta- Left. V, 
rabola A CD; or any other e Parabola i as A E F, according to the 
Angle of the Direction it Jets out with. 

GOROLL A R T I. 

Hence it follows, that one may at any time know to what 
Height a Projedile, as a Bomb, or Gannon Ball, &c. ( whether fliot 
up direclly or obliquely ) has rifen. For if you take the Time 
between the firing the Mortar and the falling of the Bomb, the half 
of it will be the Time of the Fall of the Bomb. Square the num- 
ber of Seconds in that Time, and you will have the Rods or Spaces 
fallen thro' in perpendicular Height. Thus if 20 Seconds are e- 
laps'd from the firing of the Mortar to the Fall of the Bomb, 
half that will be 10, the Square of 10 is 100, which hundred 
Rods multiplied by 16 and a half will give the utmoft Height of 
the Bomb in Feet, viz. i6$c. 

N. B. We ftill abftrattfrom the Rejiftance of the Air, which 
we fhall hereafter confider and/hew how to allow for it, as like- 
wife we take 16 £ Feet inflead i6 9 1 for the Reafon above given. 

GOROLL A R T II. 

Hence alfo follows, that knowing the Weight of a Body and 
the Height from which it falls, one may know what Stroke it will 
give ; that is, what Momentum it has "at the End of its Fall ; for 
the Square Root of the Spaces will always give the Velocity, which 
being multiplied into the Mafs and Weight of the Body give us 
its Momentum. * • . . % 

S o m e People have imagined that a falling Body has a Momen- 
tum, and ftrikes a Blow, proportionable to the Height from which 
it falls; for Example, that a Pound falling from an Height of 4 Foot 
has four times the Moment um that it would have falling from one 
Foot. But their Error lies in not taking the Time into confiderati- 
on; for a Body fpends twice the Time in falling 4 Foot that it 
does in falling one Foot, fo that the Velocity is only double in the 
firit Cafe. Indeed if a Body could fall 4 Spaces, or in any Direc- 
tion whatever go thro' 4 Spaces, while another Body of equal Mafs 
went thro' but one Space ; it would then have four times the 
Momentum, and confequentl^r be capable of a quadruple Effea. 

""t 2 Others 



Ann. 4 



328 A Courfe of Experimental Philofophy. 

Le£h V. Others again allow that the Velocity is as the Square Root of 
the Spaces ; but alledge that the Momentum is not as the Product 
of the Mafs by the Velocity of the moving Body, but as the Mafs 
multiplied into the Square of the Velocity ; which Opinion they 
endeavour to fupport by feveral Experiments, and various Reafon- 
ings, many of which I fhall confider in the Notes. * I fhall on- 
ly take notice here, that tho* I do not think the Experiments of 
hard Bodies, falling upon foft Subftances (to be hereafter more 
fully defcnbM) conclufive in Refpefl: of the Momenta of thofe Bo- 
dies; yet they have very well prov'd that yielding Subftances or 
foft unelaftick Bodies yield to a Blow of the fame percutient Bo- 
dy in proportion to the Square of its Velocity ; and thence may 
be drawn very ufeful Conlequences applicable to the Practice of 
Mechanicks. 

I isr explaining the A£Hon of Gravity upon falling Bodies we 
have confider'd it as a£Hng upon Proje&iles always with the 
feme Force, tho' it is certainly weaker in its Effect the higher 
the Body afted upon is above the Earth, as we have ihewn in 
*L,i.An.n.the 1 \th Annotation to- Left. I. * For Gravity (that is, its accel- 
lerating Force) decreafes, as the Squares of the Diftances from 
the Center of the Earth encreafe. But as the greateft Height to 
which we are able (even with Gun-powder) to projeft Bodies, 
bears no Proportion to the Diftance from the Center of the Earth, 
(fcarce one ^oooth Part) we could make no Allowance for that 
Decreafe of the Force of Gravity, without making too much, fince 
the Difference is infenfible. 

1 7. I f the Force of Gravity was greater or lefs than it is here^ 
Bodies wouM be accelerated by it in their Fall in the fame man- 
ner that we have explained ; only the Spaces which the falling 
Body goes thro' in the fame Time, wou'd be greater or lefs in 
Proportion. If the Force of Gravity was 4 times greater, a Body 
would fall 4 Rods in the 1/ Second of its Fall; and if the Force of 
Gravity was four times lefs (as it wou'd be if we were carried up to 
the Height of 4000 Miles, or remov'd farther from the Center: of 
the Earth than we are, the Diftance of one Semidiameter of the. 
Earth) a Body would fall but a quarter of a Rod in the firft Se~ 
^l. T:. Ann Gon d of its Fall. * And if we obferve, that in any Place; on the. 
Surface of the Earth a Body falls not fo great a Space as one Rod 
in & Second ; we may be fure that the Force of Gravity is lefs 

there 



A Courfe of Experiment®! ¥Mqfbphy, 

there than in our Country where Bodies fall one Rod in a Seeond. Ee6f 
Now this Obfervation has been made very near the Equator, .-**~\ 
where ftom Experiments made on Pendulums it appears that Bo- 
dies do not fair a Rod in a Second; and it; follows from thence 
that the Force of Gravity is left there than in greater Latitude^ r 
which happens becaufe the Surface of the Earth is; higher ( that is, 
farther remov'd from the Center there than at the Poles) about 

3 i Miles. But I fhall fpeak more fully of this in another Place* 
In the mean time, I refer the curious to Sir Jfaac Newtotfe, 
Trmctpia^ Book g. Prop. 20. and th& BhiloJtyhkal ^ 

No. 386, 387, and. 388.. 

18. f h e n a/ Body runs down an inclin'd Plane, it cannot deft 
cend with its whole Gravity, becaufe Part of it is fopported by 
the Plane, and that in Proportion of the Length of the Plane to 
its Height (or of the Radius to the Sine of the Tingle of Incli- 
nation) as has been fhewn in the ytb Annotation oi Le£K 3. But 
then that Part of the Weight which is not Supported by tlie Plane^ L.3,^ 
or the relative Gravity being: always of the fame Quantity, be- 
caufe every Part of the Plane has the fame Inclination, will caufe 
the Body that rolls down to accelerate its Motion in the fame 
manner as a Body that falls freely down, but not fo fail ; or in the: 
fame manner that Bodies would tall freely if the Force of Gravis 
ty was fo much .. lefs.; 

C O N S T R XJ C T I O K. > 

Upon any ftreight horizontal Line as C Bj ^ raile d Perpen- ^ pi. 
dicular at C, and make A B the Hypotenufe of the Triangle 13 * 
A B C ( which is to reprelent an inclm'd i lane) in Length equal: 
to twice the Height or Perpendicular A C Divide A B into 

4 equal Parts marked by the Points D, F, G, and iikewife A C 
into 4 equal parts, marked .. by the Points E, H, L Draw E D 
and C D. 

If A E, E H, H I, and I C be the 4 Spaces ( or Rods ) which 
a Body falls thro v in 2 Seconds, A E will be one Space which 
the Body goes thro- in 1 Second, f Now if. the /Force of Gravi-f No.> 
ty was fauc half of what it is, the Body, inftead of i going down 
from A to C in two Seconds, would only go from A^to El Let 
the Body be. laid , upon the Plane A B, , and then it wi& be* fo flip- 

ported 



&e{fe: V^pQrted by the Plane as to defcend towards B with only half its 

^fy^^M'^^ * c will lofe half its Weight and advance towards 

,2S " ' the Center of the Earth no fafter than it would do in the Line 
: Jk Q if ifcfMl freely down and the Force of Gravity \fas but half 
of what it hi-- The Body therefore rolling on the inclined Plane 
ViM come down hut to D, which is upon the lame L^vel ( or as 
near the Center of the Earth) as E ? in q Seconds. Whereas, if 
it had not been fupported by the Plane/ it would have fallen 4 
Spaces or down to C. It has then at D the fame Velocity which 
% Body falling ireely from A has at E, but is (in this Cale) twice 
as long in acquiring that Velocity. If the Body, when it is 
come down to D, continues to move along the Inclined Plane, it 
will for the Reafons already altedg'd go thro' the next 3 equal 
Spaces D P, F G, G B, in the next 2 Seconds of Time ; juft as 
a lody felMng fbeely in the Line A C would do if the Force of 
Gravity was but half ; or as a Body will do now with the whole 
$orce of Gravity in half the Time : and the Velocity of the rol- 
ling Body when it is at B will be as great as the Velocity of the 
Bqdy m C ; but it will be fo mijeh longer acquiring it as the 
Line ABb longer than A C 

CO R O L L ART L 

Hikce follows, that whatever the Inclination of the Plane is, a 
Body will have acquired the fame Velocity when it comes down to 
the Bottom of it as if it had fallen along *he Perpendicular; and if 
any two Points (as E and D, H and F, I and G) be taken in the 
l^oae horizontal Line,- one upon the Inclined Plane and the other 
Wppn the Perpendicular, the Body will have the fame Velocity in 
bath, tho' acquired in different Times. For if the Plane be lefs in- 
cline the relatk^ which carries it down will be greater, 
aiDd accelerate the Body fo much quicker as the Plane is Sorter ; 
whereas the more inclin'd or the longer the Plane % the more flow 
its Acceleration will be. 

C 0 R 0 L L ART II 

Hbhge follows alfo, that if a Perpendicular be drawii from any 
Point of the .Line m -which a Body fails freely to the inclined Plane, 
ifc will fhew how far upon the incline Plane another Body wouM 
roll la the fame Time, if the Fall of both began from the fame 

Point® 




Pipit, that is, in this Cafe C D, which frorn the Bottom of the Left, V. 
vertical Line A C comes upon the inclined Plane at D ( to which UOTWi 
Joint we have (hewn that a Body would fall along the Plane, in ^ 
the feme Time that it wouM fall freely as low as C) is perpendicu- 
lar to the Plane A B. For fince by Conftru&ion A B is the double 
of A C, and A C the double of A B, and the Angle G A D com- 
mon, the Triangles C A B and C A D will be fimikr f and eonfe- t By 6. & 
quently C D is perpendicular to A D. Euclido 

CO' ROLL ART III. 

Hence alio may be fhewn, that if aBddy ftiou*id ML down • 
the fame Height along feveral Planes different!)? kclin'd one after 
another, as for Example the Planes A D, D E, E B, fit would jiave + pi. 2S , f. 
acquired the &me Velocity as if it had fallen aloiig only (me Plane* 4- 
as A D, or the Perpeftdicular A G. 

CO RO L L AR T IV. 

It k likewife evident that if a B C4rde> 
it will have the lame Velocity at Bottom, as If ij: had fyien in the 
Perpendicular ; beeaufe an Arc of a Circle ^ m^ 
infinite Number of Planes differently inclined. 

1 8 The Do&rine of Pendulums is naturally deduced from what 
we haver explained about the Fall of Bodies y but as there are £ jme 
Things in it that require the undemanding the sd Law of Moti- 
on, we muff defer it till that Law is explained. In the mean time 
we will give an account of thole Mechanical Organs or Inftruments 
which were omitted in the 2d Le&ure (when we defcrib'd the fim- 
pie Machines ; commonly > but erroneoufly / caird Mecbamcal Pow- 
ers): becauie the Principles exp lainM in that Le£ture were not fofii- 
cient lor -it, without the knowledge of the 1 ft andS^J Law of Na* 
ture* 

10. Tpie feven fimple Machines or Mechanical Organs which I 
defcrib'd in my Second Le£tureare only Inftruments to perform the 
fame thing different Ways,— namely to convey the Powers exerted 
or fpent by fome Body acting, fo as to be applied for the moving 
of other Bodies, or to tranfmit or regulate the Power from one Body 
to another. Now the Inftruments I am about to defcribe will alio 

ferve 



33 2 Courfe of Experimental Philo/bphy. 

iLe£fc, V.ferve to perform this, therefore they may very well be calPd Me- 
wvw ehanical Organs ; but the difference in the ading is this : In 

Machines or Organs already defcrib'd, a great Part of the Strength 
of the Men or other Animals, fifcv (that is, the Xntenfity of the Pow- 
er) is loft in the rubbing, flicking, ftretching, wearing, and yield- 
ing of the Parts of the Machine, and the Force of the Men, &c. 
employ'd can only be exerted by degrees, with the lofs aforefaid. 
But in the Machines I am about to defcribe, the Power is colle&ed 
and eonvey'd from Body to Body with little or no Lofs by Accu- 
mulation continuing in the fame Line. 

2c. If a Man weighing 140% prefTes with his whole Weight, or 
exerts a Force equal to his Weight, upon a Leaver or Balance- 
Bearn equally divided by its Center of Motion, it is impoffible 
for him to overcome a Refiftance greater than Meifc, tho' 
he fliould aft upon the Beam a whole Day with all his Force, 
the Man's Power or Force being deftroy'd as faft as he ex- 
erts it; but if he can communicate his Force by Degrees to a 
Body that fhall keep it all and exert in a Moment the Sum of 
all the Impulfions given by the Man at feveral times, that whole 
Force of the Body fo colle£ted, and as it were condensed, will 
ppfbrm at once what the Man could never have done by an En- 
gine in the common Way. Such a Body was the battering Ram 
of the Ancients, which was a very large Piece of Timber (one 
of which we have defcrib'd in the %d Annotation of the 2d 
* L a - 'Leaure*) headed at one End with Metal, either Brafs or Iron, 
which was contrivM various Ways to be fupported, and by the 
conjoyn'd Strength of many Men made to be movM with the 
Metal-headed End forward ; till havirig received and kept all the 
fucceflive Impreffions of the Force of the Men (which was whol- 
ly employed to move the Ram forward ; becaufe its Weight 
was fufpended by Ropes or Chains from a Diftance above it to 
allow it t fwing freely it had by little and little acquired a certain 
Degree f Velocity; and with that Degree of Velocity it met with 
or (truck the Walls or Fortifications of Cities or Caftles, and there- 
by removed or beat them down.* This Machine is by the 

Men 

* "No doubt but the fir ft Invention of the battering Ram was copied from Nature, rather than ma- 
the?natical, Reafoning; } that is, fkom what a Ram is obferv" d to do by Inftin&l . If that Creature, 
having in vain pu/h^d with his Head againft an Obftacle by help of the Mufcles that 'extend his 
Legs, his bind Feet being fix'd hard againft the Ground, makes a fecond Attempt ; and, by a fudden 
Stroke of his Head 9 removes the Obftacle which refifted too much before : in fuch a cafe afterwards, he 

retires 




Men accelerated in an horizontal Direction m the Manner that Led. V. 
falling Bodies are accelerated by Gravity in a vertical one. The ^^^^ 
Man therefore that fhould be unable to overcome a Refiftance 
greater than 140 lb by the common mechanical Organs? might 
do it by a heavy Body fwinging horizontally in fuch a Manner 
that he could give it a Motion accelerated till it reached the Ob- 
ftacle ; that is, he could do it by means of a fmall battering Ram. 
And if it was required to have a Force imprefs'd downwards, he 
might overcome the Refiftance by the Rammer or heavy Body 
made ufe of to drive Piles into the; Earth; where applying his 
Force fucceffively againfl: Gravity (that is, raifing the Body to 
a certain Height) the Rammer would be put into fuch a Situation" 
as to receive an accelerated Motion from Gravity before it aflied 
upon the Refiftance, which at laft it would do with a great Force, 
becaufe the fame Quantity of Matter would move with a great 
Velocity; fo much the greater, as it had fpent more Time in fal- 
ling, by reafon of the Height it had been raifed to. N. -B. It 
would he wrong to alledge here, that a Man, who could not raife 
a Weight j or overcome a Refiftance fomething greater than 140th 
with the Force 140 by means of a Leaver or Beam whofe Bra- 
chia are of equal Length j might do it by applying his Tower 
farther from the Center of Motion ; becaufe we are to fuppofe the 
Weight or Int en fity of the Refiftance to be always in a ^Proportion 
to the Tower fomethtng greater than the reciprocal Troportion of 
^Diftances : that is, we are to fuppofe in this Comparifon^ a Cafe 
impoffihk in the common Ufe of mechanical Organs." 

20, The Mall or Hammer, which is a Body or Mafs of Wood 
or Metal dire£ted or movM circularly or in a curve Line by the 
Handle, fo as by degrees to receive a certain Velocity and there- 
by to have a Power of moving, or making Impreffions on, other 
Bodies, partakes of the two above mentioned Organs,, as it re- 
ceives an accumulated Force from the Arm that moves it, and at 
the fame Time from Gravity, when it is made ufe of to ftrike 
downwards. Tho 9 it is mov'd circularly, yet its Stroke is made in a 
flxeight Line, namely in the Tangent to the Curve in which it 
moves, juft at the Point of the Curve in which the Blow is made ; 

retires fo far as to be able to accelerate his Motion tQ t the.utmofl that his "Nlufcles can exert their ASiion 
in running, and thereby gives a prodigious frong Blow by the accumulated force with his am? d 
Head, to the Thing or Animal which he runs againfl ; his Horns being fo placd and fix" J on his Hea 'd 9 
that he feels no Pain from the Shock, 

U 11 becaufe 




A Conrfe of jzxpefmental Phihfophy. 

Led. V. becaufe all Bodies mov'd in a Curve endeavour to fly off in a 
Tangent to that Curve as we have already fhewn. * 




* 



2 1. The Fly (forne of whofe Ufes I have already confiderM 
l. 4. p. in the Aph * Le&ure) is an Organ whereby the Body mov'd is 
45, & m 6 - caused to circulate or move round about a Center or Axis, and 

thereby is capable of accumulating the Powers imprefsM upon 
it by degrees, fo long as {hall be required. This differs from 
the Hammer and the Mall in this Particular, as the Capftane dif- 
fers from the Leaver ; for whereas the Leaver can only lift or 
remove the Body for a very fhort Space, the Capftane can 'per- 
form it for a given or required Space. So that the Hammer or 
Mall can only receive fo much Power as can be given it in the 
Part of an Arc or Circle, or in a ftreight Line of a fhort 
Length; but the Fly can acquire its Power by Accumulation in 
many Revolutions, and fo is made receptive of a given Power 
and Velocity, and can exert the fame on any other Body in a 
determinate Manner. 

22. This mechanical Organ joyn'd to the Screw compofes that 
powerful Machine whereby they imprefs the Stamp or Image 
lipon Coins and Medals, which requires a prodigious as well as re- 
gular Force and Power. Now in this Engine there are accumula- 
ted Powers, by three mechanical Organs; firft, By the Fly, where- 
by the Srength of the Man moving it is accumulated into the 
Weights at the End thereof : fecondly, That Power accumulated 
is condensed and imprefs'd on the Cylinder of the Screw by 
means of the Radii of. the Fly, which are two Leavers that 
ferve to condenfe the fame in a given Proportion : thirdly, That 
Power fo communicated to the Cylinder accumulated and con- 
densed, is again condensed by the Slope of the Screw in a given 
Proportion ; and fo the whole Power (or all the fucceffive Powers) 
exerted by the Man in moving the Weights ©f the Fly, is accu- 
mulated and condensed in the laft Impulfion, which is made upon 
the Medal. 

23; Analogous to the Fly may be accounted the circular 
Tendulum^ w 7 hich is a mechanical Organ, whereby Motion may 
be accumulated into the Body or Weight thereof; which is fuf- 
pended by a String from a Center above, that keeps it at due 
Diftance from the faid Center. 

By 



A Courfe of Experimental Philofophy. 3 3 5 

By this Organ, the Weight to be mov'd by the imprefs'd Led. V. 

Force, is more free to receive and retain the accumulated Power, 

and receives none of the firft Impediment of the Fly, namely 
from the rubbing and wearing of the Pivots or Gudgeons, and is 
only fubje£fc to the latter, namely the Impediment of the Air 
or of the Medium thro 1 which it is mov'd, which is alfo lefs, by 
reafon that the String by which the Weight is fufpended is lefs 
than the Arms or Branches of the Fly ; and hence it is, that 
this Organ preferves the imprefs'd Force much longer than the 
other, namely the Fly, and will continue in Motion much longer. 
When fet a going it will often continue to move many Hours to- 
gether; and, if the Length of the fpiral Space in which it moves 
be computed, it will amount to feveral Miles in Length. But 
not having yet given any account of the common or Jimple Ten- 
duluMj 1 mujl defer faying any more of the circular one till I 
come to explain the Jimp le one. 

24. The laft of thefe kind of Organs that I mean to defcribe 
now is the Sling ; for the Bow in its A&ion depends upon the 
%d Law of Motion, and therefore cannot properly be treated of 
till we have explained that Law. The Sling^ then is an Inftrument or 
Organ which ferves, by the means of Strings to convey gradually 
the Strength of an Hand moving in a fmall Circle to a Body de- 
tain'd by thefe Strings, to move in a greater Circle about the 
fame Center, till it has fully accumulated in it all the Power of 
the Hand, or the defign'd ^ Quantity of it, at which Time it dif- 
charges it with a defign'd Direction and Determination. This In- 
ftrument partakes of the Fly and the circular Pendulum ; for like 
the Fly it can receive an Accumulation of Power for many Revo- 
lutions, and like the circular Pendulum it is free from the Fridion 
of Pivots and Gudgeons ; and none of the Force apply'd to it is 
loft, but juft what is fufficient to overcome the Refiftance of the 
Air. 

It wou'd be too long to defcribe the various Ways that this 
Organ has been contriv'd and made XJfeof by the ancient as well as 
the modern Engineers. It is fufficient to obferve that they are all 
reducible to this (the common Sling) which is themoft fimple ; and 
the Power and Effeft thereof is as eafy and reducible to Geometri- 
cal Computation, and Calculation as any of the others already men- 
tion'd. There being only one way applicable to all ; and it is to 

U u 2 find 




33^ <A Gourfe -of Experimental P 

Left. V.find what the Velocity of the Body isjuft at the Inftant that the 
Percuffion is made, f or the Machine apply'd to Ufe. For it be- 
4 ' ing always fuppos'd that we know the Weight of the Body or In- 
ftrument, we have nothing to do but to multiply it by the Veloci- 
f l, 2. N 9 . ty and it will give us the Momentum of our moving Body, f and 
2 > 3' thereby fliew the EfFe£t which it is able to produce in acting up- 
on another Body, in -flopping, driving, brealdng^^ ftnking it, ib 
as to fhake, move, or remove the whole or any part of it. 

2?. No w all the Difficulty confifts in finding what is the real 
Velocity of the percutient Boay juft at the Moment of Percuffion ; 
and it may be done in the following Manner, which we will firft. 
fhew with refpe£t to the Rammer or heavy Weight to drive Piles, 
it being moft eafily confidered in that Inftrument, and all Cafes 
deduced from that. 

* pi. 25. f. The 1 sth Figure of Tlate 2 5 * reprefents an Engine to drive 
* s% Piles, confifting of the Cill K I and Frame F L ? on which are fix'd 
the upright Pieces L H and L G, fupported by the Side Braces C 5 
C, and the hind-Brace F E (which has Pins on it to make it ferve 
as a Ladder) and held together by the fquare Collar E D. The 
Rammer A being a vfery heavy Piece of hard Wood or Iron Hides 
up andT down between the Cheeks or ^upright Pieces L H, L G, and 
is drawn up by means of its Hook B with two Ropes H O, G O, 
liaving each 5 fmaller Ropes with Handles at N, N, for 10 Men 
to pull up tlie Rammer to a certain Height (the great Ropes run- 
ning crtkt two Pullies or Rollers on the Iron Pin H G) and then 
let it fall again all at once upon the Head at M to drive 

it into "thfe Ground. Now fiippbfe the Rammer A weighs 500* 
and falls the Height of one Foot, it will fall that Height in a quar- 
ter of a Second, and'confequently have a Velocity able to carry it 
tN0.15.C0r. uniformly 2 Foot in the fame Time, f (that is, at the Rate of 8 Foot 
3 . P . 324. j- n a Second) at the very Inftant that it ftrikes the Pile M. There- 
fore multiplying the Mafs' by the Velocity, viz 500 X 8, we' 
fhall have 4000 for the Momentum of the Rammer, with fuch a 
FalL But if 'the Rammer be raisM up to the Height of 4 Foot, it 
will fall that Height in half a Second, and have at the Time of 
Percuffion a Velocity totarry it 8 Foot in half a Second, without any 
farther Help from Gravity ; fo that we muft now multiply 16 Foot 
(the prelent Velocity, fince it goes at the Rate of 16 Foot in a 
Second) by" 500 the Mafs of -the Rammer, which will give us a 

double 




A Courfe of Experimental 

< 

double Momentum wherewith it will ftrike the Pile in this lallLe£t. V, 
Cafe; for 500 X 16 — 800c. If we confider any other Height (>YV 
from which the Rammer falls (for one * may ehiploy a Capflaney 
Windlafs/or Pul]ies ? to raife jt to a very great Height, and then 
by an eafy Contrivance loofen it at once from its Mook) the Momen- 
turn j with which it ftrikes the Pile, will always be as the fquare 
Root of the Height from which the Rammer fell; that is, as the 
Velocity which the defcending Body has at the End of its Fall 
N. B. / cannot fay but that the Tile may enter into the Earth 
fometimes farther than in that "Proportion ; hut I Jhall jhew the 
Reafonofit in the Notes.* * Ann. 4* 

0.6. I f a Pile is to be driven obliquely ; the Engine muft be fet 
fo that the Cheeks may have the fame Obliquity, and the Blow will 
ftill be perpendicular to the Head of the Pile ; but then the Force 
of the Blow muft not be eftimated from the Length, but from the 
Height, of the Defcent, in the manner already fhewn ; becaufe 
how long foever the inclined Plane is, in which the Body falls, it has 
acquired no more Velocity than what it would do if it had only fal- 
len perpendiculary from the Height of the Plane. 

27. To find the Velocity of the battering Ram when it makes 
its Stroke, we muft obferve at what Rate its Motion is accelerated; 
for according to the Number and Strength of the Men that work 
it, it may be accelerated more or lefs than Gravity would accele- 
rate it if it was to fall perpendicularly. Therefore we are to ob- 
ferve the Length of the Stroke from the Point moll: remote from 
the Wall (or the Thing batterM) and the Wall, and take notice 
in what Time the Stroke is made (for when the Men, by a little 
Praftice, have got the Knack of playing the Ram, all their Strokes 
are made in the fame Time) if the Stroke, for Example, be of 4 
Foot and made in a quarter of a Second, the Momentum of the 
Ram is equal to what it would be if the fame had mov'd uniform- 
ly 8 Foot in a quarter of a Second, or 32 Feet in one whole Se- 
cond. This Force would be quadruple of what Gravity might 
give the failing Ram (or a Rammer equal in Weight to the Ram) 
in r thje;vfeiWe Time; but only equal to what it would give it in one Se- 
condor the quadruple of the Time; and only half of what Gra~ 
l^i ty ^ \i^iilcj : give in. two Seconds to the lame Body falling from an 
Height ^ than 64 F efete If the Time of making the 

Stroke had been twice as long, or half a Second^ then the Momen- 




A Cowfe of Experimental Philofophy* 

. turn or Force of the Percuffion would have been but half as great 
> &c. the Percuffion with the fame battering Ram being always in- 
verfely as the Time in which it is accelerated by the -fame Force 
of Men, 

28. To find the Velocity (and confequently the Momentum) of 
the Mall or Hammer at the inftant of Percuffion, we mud confi- 
der it firftin the moft Ample manner,, as when being rais'd up it 
falls down again in an Arc of a Circle by its own Gravity: then 
we are only to confider the Height from which it fell; and we 
fhall know, from what we have laid of Bodies falling perpendicu- 
larly or on an. inclined Plane, what Velocity it has at the end of its 
fall. Thus we may know with what Force the great Hammers, 
rais'd by the Axis of a Water-wheel, fall upon the Plates or Bars 
of Iron or Copper that are flattened in Iron or Copper Battering 
Mills or Forges. When the Hammer is movM by the Hand, or 
driven by a Spring as well as by Gravity, it will move quicker, and 
its EfFe£fc will be proportionably greater, therefore by ooferving the 
Time of its Fall in fuch a cale, its Velocity may be known. N. B. 
Tho* a Body, moving twice as fafl in the fame Circle was able, 
according to what appeared in the i$th Experiment of this 
LeBure, to raife 4 times the Weight ; we mufl not imagine that 
a Hammer mov'd twice as fajl will flrike with 4 times the Mo- 
mentum, whilfl a Hammer of the fame Weight moving twice as 
fafl, only becaufe of an Handle or Radius twice as long, /hall have 
but double the Momentum according to the i%th Experiment $ 
for it is only the centrifugal Force in the fame Circle, which is 
as the Square of the Velocity, and not the Stroke made along the 
Tangent. The EjfeEl of the centrifugal Force will only be this, 
that the Hand which holds the Hammer will feel 4 times the 
Force endeavouring to pull the Hammer out of his Hand j and 
would feel but twice that Force if the Velocity was only double 
by having an Handle twice as long. 

It is alfo to be obferved, that in the ufe of the Hammer it is 
better to firike with the fame Mafs of Matter with a double 
Velocity j than with double Mafs and fingle Velocity $ becaufe 
yielding Subfiances, as hot Iron, Sfc. and Nails driven into Wood, 
give Way to the fame Hammer nearly according to the Square of 
Ann. 4. its Velocity, as we fhall \ accouitt for in the Notes , * But the Re- 

verfe 



M Courfe of Experimental Phikjbphy. 3 3 

verfi mufl he done in the Battering Ram, if you would have *£iLe£t. 
greatefi Effe£t.\ 

29. If the Fly be made ufe of only to give a Blow with one of 
its Weights after fome Revolutions, the Method of finding its Ve- 
locity, and confequently its Momentum, juft at the Stroke, is the 
fame as will ferve for the Sling ; for tho' the Fly has vaftly more 
Fri£tion than the Sling, we are only to ohferve what Velocity 
(without any regard to the Impediments which, hinder'd the Velo- 
city from being fo great as if would have been without them) it 
has juft at the Stroke ; which we may know by comparing feveral 
Revolutions, or Parts of Revolutions, together ; which will fhew us 
the Degree of Acceleration. 

■30. No w to fliew how to calculate the Force of thefe Organs 
when joyn'd with others commonly called the mechanical lowers 
(explained in the ad Le&ure) I fhall fhew what Force may be given 
by the Machine made of the Fly combined to the Screw for damp- 
ing the Image upon Coins, as we have above hinted. 

Let us fuppofe the two Arms of the Fly to be 15 Inches long 
each (meafuring from the Center of the Weights to the Axis of 
Motion) and the Weights to be 50 lb each, and the Diameter of the 
Axis preffing upon the Dye to be one Inch. If every Stroke be 
made in half a Second, and the Weights defcribe an half Circumfe- 
rence, which wilt in this Cafe be of a Foot, the Velocity will at 
the Inftant of the Stroke be at the Rat6 of 3 Foot in a Second, 
and therefore the Momentum of it will be Sop ; but the Arms of 
the Fly being as Leavers, one Brachium of which is 1 5 Inches long, 
whilft the other (which is the femi- Axis) is but of half a^i Inch, 
we muft encreafe this Force 3 o times, which will give us £4000 : 
an immenfe Force, equal to 1 oolfe Weight falling 1 20 Foot, or near 
2 Seconds in Time, or a Body of 750Tb falling ifh Foot or one 
Second in Time. Some of thefe Engines for coining Crown Pieces 
have the Arms of the Fly 5 times as long, and the Weights twice 
as heavy ; and the Effeft is 1 o times greater. 

N. B. We have allow" d nothing here for the inclined Tlane of 
the Screw, becaufe that 'Declivity only ferv'd to help to ac- 
celerate the circular Motion of the Weights, which we co7tfi~ 
der'd in taking the Time of the T^ef crip ion of the- Semicircle 
by them* 

21. 







ourfe of Experiment a 



Left. V. gr. It would be endlefs, to fhew all the Conferences of th§ 
two Laws of Motion already explained, in the Practice of mecha- 
nical Operations ; and to apply them to the Explication of all kinds 
of Motions whether of Bodies on Earth, or of the Planets and 
Comets in the Heavens : We fhali only give a few Inftances more ; 
but firft we mull fhew how far the Refiftance of Air (which we 
have hitherto left out of our Computations) hinders the Effe£ts from 
being fuch as might be expected from their Caufes without it. 

T h o' the Refiftance of Mediums is to be confiderVl in the Hy- 
droftatical Part of this Work, yet we muft fay fo much of it now as 
is required for underftanding how to allow for the Difturbance that 
the Refiftance of Mediums gives to moving Bodies, whether their 
Motion be owing to Gravity, or any other Caufe or Caufes. 



i . Wh e n a Body moves in a Fluid of any kind whatever, or 
refifting Medium^ it cannot go on without feparating the Parts of 
the Medium to make it felf Way ; and fo much as it beftows of its 
own Motion on thofe Parts, fo much it lofes of its own Motion; 
fo that it will be retarded if its Motion was uniform before ; or if 
it went on with an accelerated Motion, that Refiftance (or the Moti- 
on given to the Parts of the Medium) will hinder the Acceleration 
from being fo great, as it would have been, or (according to the 
Qiiantity of it) deftroy the Acceleration ; that is, deftroy the additio- 
nal Motion as faft as it is given to the Body by the accelerating 
Caufe : fo that the Body will then move uniformly ; as if the acce- 
lerating Caufe had ceafed to a£t, and the Body fhould move in a 
Vacuum without any Refiftance at all. 

\ 

i 

32. There are two forts of Refiftance in Fluids the Firft a- 
rifingfrom the Tenacity of the Fluid, that is, from the Cohefion 
of its Parts ; and that Refiftance is always as the Velocity of the 
Body moving in the Fluid ; for the fwifter the Body moves in fuch 
a Fluid the more Parts it has to remove from their Cohefion in the 
^fame Time according as it goes thro' a greater Space. That fort 
of Refiftance may be diminiflhM by rendring the Medium more 
fluid, as Oil, Honey and Pitch, &c. become more fluid by heating. 
N. B. Such Fluids as have no Tenacity have none of this Rejif 
tance. 

The other fort of Refiftance arifes fi|pr the Qpantity of Mat- 
ter to be remov'd, and that is always piOf #tiona^to the Denfity 



A Courfe of Experimental Phibfophy. c 

or fpecifick Gravity of the fluid Medium. Thus Water refills 8 50 Led. V. 
times more than Air, becaufe a Body moving in it thro' a certain ^-nr^ 
Space, has §50 times more Matter to remove ; and ifitmov'dm 
Mercury, the Refinance would be 1 1 900 times greater, becaufe 
Mercury has 11900 times more Matter than Air in the fame Space. 
In refped to the fame Body moving with different Velocities in a* 
Fluid, this Refiftance is always as the Square of the Velocity. An 
Inftance or two explain'd by Number will make the Thing eVi- 
dent. 

Let us fuppofe the Body A (TV. 25. Fig.^6.*) to be moving* pi. 25. p. 
in a Medium at the Rate of 2 Indies in a Second or from A to B, t 6, 
and that it is to remove the 4 Particles of Matter b, c, g, f, to 
make its Way, which Particles we will fuppofe to be an Inch in 
Diameter. Now it is not enough to confider that thofe Particles 
are to be remov'd, but we muft alfo examine with what Velocity 
they are remov'd in order to find the Quantity of Motion which 
they receive. Let us then fuppofe each of them to be remov'd an 
Inch in a Second or from the Points f, b ? c, g, to j\ b y c, g, to 
make Way for the Body A to go between them. Now fince it 
is the fame to move all the 4 Particles laid upon one another from 
f to /; as to move all the Four, one Inch in different Lines, it is 
evident that the Space f / or one Inch is their common Velocity : 
One then multiplied by Four the Number of Particles gives 4 tor 
the Momentum of the Matter remov'd by the Body A, which 
eonfequently muft lofe as much of its Motion as it has communi- 
cated ; and therefore in this Cafe the Refiftance will be 4. Again, 
let the fame Body be fuppos'd to move twice as faft, that is, from 
A to B (Fig. 16. ■ *) in a Second. There muft be 8 Particles (that* P1 . 2 .. F ; 
is, b, c, d, e, f, g, m, n, or as much more Matter) remov'd in 16. ' 3 ' " 
the fame Time ; but as the Body moves twice as faft, it will ftrike 
each of them as hard again, which will make them recede to the 
Points /3, y, -f', < , y 9 v , ?, inftead of the Points c, d, e, j\ g, m, « 
in the fame Time ; fo that their common Velocity will be 2 Inches 
inftead of 1. But 8 Particles multiplied by 2 will give t6, which 
is a Momentum 4 times as great as what the Matter of the Fluid re- 
ceived before. Therefore the Body moving twice as faft in the fame 
Fluid communicates four times as much Motion to its Parts, and 
eonfequently meets with 4 times as much Refiftance. Likewife if 
the Body mov-d 3 times as faft, it would remove 3 times more 
Matter in the fame Time and alfo dafh it 3 times farther ; therefore 



34 2 d Courfe of Experimental Philofophy. 

Le£h V.it would meet with 9 times more Refiftance. And this will hold 
<^YNJ> good in any Degree of Velocity of the moving Body j for the Quan- 
tity of Matter removed in a certain Time, and the Velocity with 
which that Matter is removM will always produce a Momentum in 
the fluid Medium, and confequently a Refinance, proportionable to 
the Square of the Velocity of the Body moving in that Medium. 
N. B. This Refinance according to the Square of the Velocity is 
tUe only Refiftance that the Air is found to have, by Experiments 
of Bodies moving in it : and therefore it has no Tenacity f a Con- 
fequence of which is, that its Tarts do not touch one another* 

Hence it is, that a Fluid will reiift fometimes as much as a So- 
lid, nay more, when the Velocity of a Body coming againft it is 
very great, as we fhall fhew by lome Inftances that we fhall give 
* Ann. 5. in the Notes** 

SCHOLIUM. 

33. What we have faid concerning the Fall of Bodies in the 
Air, and along inclined Planes, will not agree with Experiments, 
becaufe in the Theory we abftra&ed from the Refiftance of the 
Air ; but when we make proper Allowances for it, the Experiments 
will confirm the Theory. According to the beft Obfervations a 
Body falling in Vacuo fhould go thro' 16 Englifh Feet and an Inch 
and a quarter the firft Second of its Fall ; but in the Air it muft 
lofe of that Space in Proportion to the Motion it gives to the 
Air, which muft be fubtrafited from its own Motion ; fo that the 
more Matter the Body has in Proportion to its Surface wherewith 
it {hikes' the Air, the lefs it will lofe of its own Motion. This 
will be beft explained by giving an account of an Experiment I 
made by obferving the Time of Leaden Balls which I let fall from 
the infide of tlie Top of the Cupola in St. TauPs Church. 

E. X P E RIM E - N T XVI, 

I took feveral Leaden Balls of 2 Inches Diameter, weighing 2 th 
Troy, which I let fall from a Board fix'd 2 Foot over the Top of 
the inner Cupola, and obferv'd the Time of their Fall very nicely 
by an Inftrument which I fhall hereafter defcribe, and found that 
they fell to 1 the Bottom in 4 £ Seconds and a very little more. The 
Height was 272 Feet. Now according to the Theory, the Balls 
in that Time Ihould have fallen 5 2 Feet farther, that is, 3 24 Feet ; 

therefore 




therefore the Refiftance of the Air continually taking off fomething Le£h V. 

of what Gravity fuperadded to die Motion of the defcending Body ^\r^ 

occafion'd the Acceleration not to be fo quick, and therefore the 

Body was longer in falling that 272 Feet than it ought to have been ; 

for fince a Body falls a Foot the firft quarter of a Second of its Fall, 

if we take the Square Root * of 272 we fhall have 1 6i quarters, 

that is, 4 Seconds and f for the Time that a Body would mil 272 * No. 15. 

Feet in Vacuo. Suppofe now that the Refiftance of the Air took 

off 5 Inches of the Space which the Balls fhould have fallen the firfl: 

Second ; during the 2d Second the Refiftance of the Air muft be 

greater in Proportion to the Square of the Body's Velocity ; that is, 

as the Body then JOhould go thro r 9 Spaces equal to what it went the 

firft Second, the Refiftance muft be 9 times greater, confequently 

the Refiftance of the Air would take off 9 times 5 Inches, that is, 4$ 

Inches of the Spaces gone thro' by the Body in the 2 d Second : fo 

likewife in the 3d Second the Body muft lofe 125 Inches ; in the 

4th Second 245 ; and in the laft half Second above 200 ; which 

makes about 5 2 Foot in all, according to what was obferv'd in the 

Experiment. 

N. B. This Calculation is not exaB^ being given only as an Illuf- 
t rat ton rather than a Demonstration, and founded upon a Sufi- 
fofition of a Body falling only 1 6 Foot in the firft Second of its 
Fall) which Number was taken to avoid Fractions. 

Several Confeqnences may be drawn from the Refiftance of 
Air in regard to Bodies moving in it, and which are verified by Expe- 
riments, The Firft is, That the Motion of a heavy Body is not al- 
ways accelerated^ but at a certain Height it becomes equal and 
uniform in the Air ; becaufe the Refiftance of the Air encreafing 
in the lame Proportion as the Spaces encreafe (and confequently 
in a duplicate Ratio of the Times, or of the Velocities) this Refii- * No i2 > ar 
tance may become fo great as to deftroy as much of the Velocity 
as fhould be produced, and by that means hinder the Velocity of 
the moving Body from being encreafed any more ; * juft as if the 
Body at that Time fliould ceafe to be heavy. The Second is, That 
Bodies of different fyecifick Gravities moving in the fame Medi- 
um have not their Motions accelerated after the fime manner , 
by reafon of the difference of their Bulk, compared to their Weight, 
which meets with more or lefs Refiftance ; becaufe thofe of a great- 
er Bulk, when the Weight is the fame, drive more Air before them 
than thofe of a lefs* 

Xx 2 The 



A CouYje of Expefim^ 



Left. V. The Third is, That the Motion of heavy Bodies is differently 
accelerated in different Mediums, and in the moft denfe Medium 
it become^ equal fooneft ; becaufe the more denfe the Medium is, 
the more Difficulty it lias to make its Circulations, and it refifts 
Motion the more eafily. 

The Fourth is, That the le aft Bodies of the fame homogeneous 
Matter fall with lefs Velocity , and come fooneft to an Equality ; 
becaufe that Body which has a greater Surface is more refilled than 
that which has a lefs, and the lefs Bodies have a greater Surface than 
the great ones in refpeft of their Weight or Solidity ; for we are 
taught by Geometry, that if a Cube has its Surface, for Example, 
of one Foot, another Cube eight times as heavy will have its Sur- 
face but of four Foot. According to this Principle, the Dufi falls 
very flowly when it is rais'd, Birds fuftain themfelves in the Air 
by. fpreading their Wings ; and a Charge of Shot will not go near 
fo far as a Bullet of the fame Weight ihot from the fame Gun with 
the fame Quantity of Powder, thoVboth begin to move with equal 
Velocities, 

T h e Fifth is, That there is a determinate ^Height which pro- 
duces in a heavy Body the great eft Velocity that it can acquire in 
falling ; io that if it ihouldfall from an higher Place it wottld'liave 
no more Velocity ; which is evident from the firft Confequence, 
where we have laid that the Motion of a heavy Body is not con- 
tinually accelerated ; but that at a determinate Height it becomes 
equal. 

The Sixth is, That there is a determinate Height, the great eft 
of all thofe to which the Velocity which a Body has acquired in fal- 
ling, can make the fame Body rife up again ; becaufe by the fore- 
going Confequence, there is a determinate Height, which produces 
the greatefl: Velocity that a falling Body can acquire, and that Ve- 
locity can make it rife up again but about to the fame Height. 

[The Seventh is, That a Body thrown upwards by a Force great- 
er than the great eft that it can acquire in falling, ought to be long- 
er in falling than rifing ; becaufe the Velocity of a Body thrown 
up to any Height whatever, is continually diminifih'd ; whereas the 
Velocity of the fame Body in its Fall encreafes but till it comes to 
fuch ia Height, k being certain that if it fho&id encreafe continually, 
the Body would bejuft as long in falling as in rifing. 

The 



The Eighth is, That if a Body be thrown downwards 
that exceeds the great ejt Force it can acqtitre in falling, it will^s-^t* 
have a retarded Motion > becaufe by the firft Confequence the Body 
whicih falls with the greateft Velocity that its Fall would give it, 
meets with a. Refiftance in the Air, equal to its Gravity ; and when 
it goes with a greater Force;,/ the Refiftance of the Air becomes 
greater than its Gravity, arid muft deftroy part of the Motion,. 
Which thus will be flackened and retarded. 

Thi s laft Confequence Chews why a Cannon Ball fliot down- 
wards retards its Motion ; becaufe fuch a Ball is put in Motion by 
the Force of the Powder which gives it a greater Velocity, than 
that which its abfolute Gravity would have given it in falling : And 
the Seventh Confequence fhews likewife the Reafon of this Expe- 
riment which Father Merfennus takes notice of in his Bali/Iica, or 
Art of throwing heavy Bodies. Prof, i g. 

This Author fays, that he has found by feveral Experiments, 
that an Arrow which has been three Seconds in rifing, has been five 
in defcending j and thoMie adds that an Iron Bullet of three Pound- 
weight having been fhot upwards perpeiidiculary by a Mortar- piece 
a Foot long, has fpent as much Time in rifing as in defcending, viz,. 
Six Seconds ; yet it does not follow that it muft always happen fo, 
the Difference not being To confiderable in a Bullet as in an Arrow, 
whofe Motion comes fooneft to an Equality, by reafon of its 
Lightijefs. 

A common Bomb not receiving from the ufual Charge of Pow- 
der a Velocity greater than the greateft it can acquire in falling, is 
as long in coming down as it is in going up. But a Bail of light 
Wood or of Cork (which in a Vacuum would go much higher 
and farther than a Bomb of the fame Mgnefs, becaufe it receives 
from the Powder fo much more Velocity at firft \ as it has leis Mat- 
tel-) will not go ip high as a Bomb, and alfo will be longer in co- 
ming down than in going up, on account of the Air's Refiftanee 
which has more Effeft upon thofe light Bodies for the Reafons a- 
bove given. 

N. B. It is not mathematically true, that a Body falling in 
the Air ever comes to an equal Mdthn-s-^ut-'^sit-ali^ays 
approaches mar er md nearer to it, we> may take it to be 
fuch j>hyficallj) and reafon ftotto it accordingly* 

34- 1 



34^ A Courfe of Experimental Phihfophy. 

Le£t V. # I Chew'd, after explaining the firft Law of Motion, how far 
w*~v~s^ it would ferve to make us acquainted with the Motion of the hea- 
venly Bodies, by fhewing in what Manner Gravity and the projec- 
tile Force keep thofe Bodies in their Orbits; but it required the 
Underftanding of the fecond Law to conceive rightly how they move 
in Ellipfes that have the central Body in one of the Foci, and why 
their Velocities are fucceffively accelerated and retarded. 

35. But before I proceed to confider this, I muft explain Tome 
Aftronomical Terms, and fhew what is meant by faying, that the 
^Planets and Comets in refpell to the Sun defer ibe Area's about it 
proportionable to the Times ; as Like wife the Satellites in refpeEl 
to their primary Tlanets. And this is a Truth known and own'd 
by all modern Aftronomers, however they differ in accounting for 
the Caufes of the celeftial Motions. 

Suppose a celeftial Body to move round another in a Curve 
returning into it felf as a Circle or an Oval; as for Example, the 
Moon about the Earth, whofe Orbit we will confider at firft as cir- 
cular, tho'it is really elliptical. If- at any Time of a certain Day 
+PI.25.F.18. weobferve the Moon's Place in its Orbit to be at L -fo and the Day 
after, at the fame Time, the Moon is found to beat another Place 
as L y the triangular Space TLL (being contained by the Line or 
Ray T L drawn from the central to the revolving Body, at the firft 
Obfervation, the fame Line in the Situation T X at the fecond 
Obfervation, and the Arc L L defcrib'd by the Moon during the In- 
terval of the Obfervations) is calfd an Aftronomical Area, and the 
Ray T L, confider'd as fweeping along that Space and carrying the 
Moon with it, is called the Radius veffior or fweeping Ray. If 
fome Days after, for Example 14 Days after, we obferve the Moon 
at 1, and the next Day at the fame Hour and Minute obferve it to 
be at /, the Area T 1 / will be equal to the former Area TLZ 
which was delcrib'd by the Moon and Radius veil or in the fame 
Time : and this is what is meant by faying, that revolving Bodies 
in the Heavens defer ibe about the central ones Area's proportionable 
to the Times. 

36. Here we are to obferve that the Triangles or Area's T L Z, 
*pi.25.f.i8. T 17/ -\ are not only equal but fimilar, and therefore the Body 

L does in this Cafe defcribe the equal Arcs L L and 1 / in equal 
Times, as well as equal Area** ; fo that the Motion of L round 
T is equal, neither accelerated nor retarded Such are the Moti- 
ons 



A Courfe of " Experiment al Philofophy. 34.7 

ons of Jupiter's Satellites about his Center, their Orbits being cir-Le&. .V. 
cular (as far as Obfervations have been made hitherto) except fo <^VN* 
much as they difturb each other by their Gravity towards one ^an- 
other, and as they are difturb'd by the Sun according to the diffe- 
rent Diftances of Jupiter from the Sun, or by Saturn whofe At- 
traction becomes fenfible, at, and near, its Conjunction with Jupi- 
ter. But all thefe Inequalities may well be neglected here ; be- 
caufe, tho' they are certain confequences of the mutual Attraction 
of Bodies, they are not considerable enough to be obferv'd with 
Telefcopes. 

57. Now let us fuppofe the Body T not to be in the Center 
of the Orbit, as the Earth is not in the Center of the Moon's Or- 
bit, but to be diftaht from it the whole length C T {Fig. 19. f) j-PUs Fig. 
If the Moon or the revolving Body be obferv'd at Land L, and' 9 " 

fo found to have gone thro' the Arc L L in ones Day's Time ; 
then again if it be obferv'd 1 4 Days after at 1, the next Day it 
will not be at a (to which Point it wou'd have gone in a Day # if 
its Velocity had not encreas'd) but it will be got quite to /, its 
Velocity encreafing fo as to make it defcribe fo much a greater 
Arc as it is nearer to the central Body T; otherwife the Area 
laft defcrib'd wou'd not be equal to the Area firft defcrib'd; for as 
much as Tl, the Diftance from the central Body in the beginning 
of the Defcription of the laft Area, is lefs than T L the Dif- 
tance from the central Body in the beginning of the firft, fo much 
•muft the Arc defcrib'd in the laft be greater; that what this laft 
Area wants in length may be made out in breadth. 

58. If, infteadof a Circle, the revolving Body moves in anEl- 
lipfe, in one of whofe Foci the central Body is plac'd (as is the 
Cafe of the Moon about the Earth, but more ftriclly fo of the 
Planets and Comets in their Motion round the Sun) and the 
whole periodical Time of the Body's Revolution be divided into 
equal Parts, in every one of thofe Parts of Time the Body (by 
its Radius vector) will defcribe an equal Area, but none of thofe 
Arenas will be fimilar except thofe that are defcrib'd on each fide 
of the Axis of the Ellipfe in correfpondent Parts of the Curve at 
equal Diftances from the central Body. Let ABCDEPFG 

H I -|- reprefent one of the Ellipfes which is defcrib'd by a Pianettes F 
or a Comet round the Sun ; P S s A the Axis of the Ellipfe and 
S, x, its Foci : S the Sun, and A a Planet at the Sun's Aphelion 

(that 



548 ^ Courfe of Experimental ^ VUhfbphy. 

JUGt. V*(that is, at thegreatefl: Pittance from it) and P the fame Planet at the 
Lf^TSJ 'Perihelion (or leaft Diftance from the Sun) and the Time of the 
Revolution be divided into 10 equal Parts ; the Planet fetting out 
at A and going towards B, by its Radius veBor A S, will defcribe 
fuccelTively the i o equal Area's A SB, BSC, CSD, DSE, ESP, 
PSF, FSG, GSH, US I, ISA, of which only every two corre- 
fpondent Area's are alike, as BSC is like ISH, DSE like 
G S F, &c. 

CO R O LLART L 

Hence follows, that in an excentrick Orbit, fuch as an Ellipfe, 
the revolving Body moves fafter at the Perihelion (the Sun being 
in one of the Foci) than at the Aphelion y accelerating its Motion 
from the Aphelion to the Perihelion, and retarding it from the 
Perihelion to the Aphelion. 

CORO LLART XL 

Hence follows alfo, that the more excentrick (that Is, thelong~ 
er) the Ellipfe is, the greater is the Difference of Velocity at the 
Perihelion and Aphelion, fuch is the Cafe of Comets, which mo- 
ving in very excentrick Ellipfes, go thro' the lower Part of their 
Orbits with very great Velocity, but move extremely flow near 
their Aphelia. 

€ O R O L L A R T IIL 

This fhews why a Planet, tho'it be much more ftrongly ■ at- 
tracted .in its Perihe lion than its Aphelion, will not be drawn into 
the Sun ; becaufe it acquires a greater centrifugal Force as its Velo^ 
city increafes, and thereby balances the Sun's increased Attractions 
So likewife, when the Planet goes from the Perihelion to the A- 
f he lion, tho' the Sun's Attraction be decreased, becaufe of the en- 
creas'd Diftance, the Planet will not fly out of its Orbit; for the 
Velocity decreasing, the centrifugal Force decreafes alfo. In the 
+ pi. 25. f. Ellipfe reprefented by Fig. 20 ^, when the Planet is at P it is 
fix times nearer the Sun S than when it is at A, therefore it is 36 
l.i. page times more attracted ; but then its Velocity being alfo 6 times 
9 ' 32 ' greater, the centrifugal Force increafing as the Square of the Ve- 
t Exp. 15. loeityj becomes 26 times greater. So that the Attraction, or 

page 2U. J 7 J o > . 

^ accelerating 



20. 




e of Experimental Thilofophj. 349 



accelerating Force* (however it increafes or decreafes, on account Left. V. 
of the different Diffenee) is always balanc'd by the centrifugal Fo^ce OOTX/ 

of the Planet. ' ' ' * l. i. page 

32. 

COR O L L A R T IV. 

Hence we fee, why thofe Planets, which are neareft to the Sun, 
perform their Revolutions in fhorter Time than thofe which are 
farther off ; that their greater Velocity may give them a fufficient 
centrifugal Force to balance their centripetal Force (or Gravitati- 
on) towards the Sun ; Regard alfo (being had to their Quantity o,f 

Matter f. ■ ' i Exp. t2 . 

p. 312. 

The Satellites of Jupiter and Saturn alfo have their Periodical 
Times flic iter, as they are nearer to their Primaries, as we have 
already hinted f. t No . 7 . 

page 308. 

Tho' the Orbits of the Planets are nearly circular ; yet -as the 
Foci of an Ellipfe are confiderably diftant from one another, when 
the Curvature does not much differ from that of a Circle ; theEx- 
centricity will be fenfible enough to be obferv'd. Hence it is, that 
our Winter Half- Year (in the northern Hemifphere of our Earth) in 
which we go thro' the 'Perihelion, is 8 Days longer than the Sum- 
mer Half- Year, &c. 

39. KET LE R was the firft who difcover'd, that the Pla- 
nets, by a Ray drawn from them to the Sun, defcribM Areas pro- 
portionable to the Times ; and guefs'd that the Caufe might be a 
Gravitation towards the Sun ; but he did not demonftrate it. But 
Sir Ifaac Newton has demonftrated it in his T rjncipja, fhewing, that 
when a centripetal Force drives one Body towards another, and that 
firft Body has received the Impreffion of a proje&ile Force in any 
other Direftion, it will defcribe round this Iaft proportional to 
the Times; and vice verfd, that if a revolving Body, by a Ray 
drawn to a central Body, Mcnhes Jreas proportionable to the 
Times, it is acted upon by a centripetal ^Force. Then he fhews 
(from Obfervations of the Moon's Motion): that the centripetal Force 
is the very fame as Gravity, w'hich makes, our Bodies fall by an 
accelerated Motion near the Surface of the Bartji. We fhall give 
his Demonftrations and a further Account in the Notes f. . Ann 6 

Y y 40. In 



35° " A Com % fe oj [ Experimental Philofophy^ 

LeQy V. 4C In the mean time I fhall endeavour, in the eafiefl: way, to 
vnrw fhew ho.w Gravity makes the Planets defcribe their excentrick Or- 
bits with a Motion uniformly accelerated and retarded j for tho' I 
fhall give no ftri£fc Geometrical Account of every thing relating to 
this Motion, and the Nature of the Curve, yet every Alfeitioa 
will be a Confequence of the two Laws of Motion^ already ex- 
plained, and their Corollariese 

T late 25. Fig. 2c* 

fi aj.F. 20, Th e Ellipfe reprefented by this Figure, is more excentriek 
than any of thofe that are defcribed by the Planets, but not fo ex- 
centriek as thofe that are defcribed by the Comets. I took it at a 
Mean ; becaufe, as both the Comets and Planets are retained' in 
their Orbits, and continue their Motions from the fame Gaufes,, 
oiie Explication might ferve both. 

Let S reprefent the Sun, A the Planet or^Gomet, which Gra- 
vity (;r the mutual Attraction of the Sun and revolving Body) 
drives towards the Sun in the Direflion AS; and let AM repre- 
fent the Quantity of that Force ; that is, the Space, which that 
Force alone a£ling, would caufe the Planet to go thro' in a gi ven 
Time. Let the Planet A be fuppofed to have received a projefibile 
Force In the Direction Ax at right Angles to AS. f A a ex- 
prelfes the Space which the projectile Force alone would make the 
Planet defcribe in the faid given Time, and the Quantity of that 
Force be fuch, as afting jointly with Gravity, will make the Planet 
(fetting out in the Diagonal A m of the compleated Parallelogram 
A am M) defcribe the Circle A m ^ &r. whole Center is S the 
Center of the Sun ; then a greater Vis imprejfa t x)v proje&ile Force, 
inch as A a (the Force of Gravity A M remaining . the feme) will 
make the Planet let out in the Diagonal A \n of the compleated Pa- 
rallelogram A a n M,. and defcribe an Ellipfe. A n v, &c. whofe 
iieareft Focus is S \ then will the Point A become the Teriheliou 
inftead of the A f he lion y and the Motion will he retarded from A 
till it comes to the Aphelion on the. other Side of Su; and then 
from that Aphelion accelerated till it comes back to A, from whence 
it began its, Motion. But if, the. proje&ile Force be lefs, than 
what we have fuppofed capable of making the Planet move in a 
Circle* and it be expreffed by A. a inftead of A then the Pla- 
net, 



ACourfe of Experimental Phihfophy* jjg.i 

net (beginning its Motion in the Diagonal A B of the compleated LeCh V. 
Parallelogram A a B M) will defcribe the Ellipfe ABCDE PF GH -^~v~^ 
I A, the Sun S being in the farther Focus, and the neareft Focus Flzs ' F * zo ' 
will be at s j fo that now A will be the Aphelion, and P the T e-* 
rthelion. 

N o w to fhew how the Planet is accelerated in going from the 
Aphelion to the Perihelion s let us obferve that at firft letting out, 
the Direction of the projeCtile Force A oc is at right Angles with the 
Direction of Gravity (or the centripetal Force) A S. When the 
Planet by the joint ACtion of the two Forces is come to B ; the 
projeCtile Force has its new Direction along the Tangent B b, which 
makes an acute Angle with the new Direction of Gravity which 
now is B S ; therefore the Planet will defcribe a longer Diagonal 
in the fame Time,*- viz. B C, that is, encreafe its Velocity fo that* No - 
the Area B C S may by a Breadth proportionably greater be equal 
to the longer Area ABS. When the Planet is come to C, the 
Direction of the projeCtile Force along the Tangent C c ftill making 
an acute Angle with C S the Direction of Gravity, the two Forces 
confpiring ftill accelerate the Planet and carry it from C to D 
in the lame Time that it went at firft from A to B. The fame 
Forces confpiring ftill in their Directions D d and D % when the 
Planet is at D ? will in a Space of Time equal to the former carry 
it to E : and laftly, the fame Forces with their confpiring Directi- 
ons will ftill accelerate the Planet in its Motion from E to its 'Pe- 
rihelion P, where its Velocity is the greateft of all. At P the Pe- 
rihelion, the Direction of the projeCtife Force is along the Tangent 
P /, and makes a right Angle with P S the Direction of Gravity ; 
and the Planet from the Action of thofe two Forces will go to F. 
When the Planet is at F, the Direction of the projeCtile Force along 
the Tangent F / makes an obtufe Angle with F S the Direction $ 
Gravity ? and therefore the Motion of the Planet muft be retarded, 
* becaufe the Diagonal F G will be fhorten'd, as the Angle fF G* No. ^/ 
opens, and the Forces begin to aCtagainft one another. The Angle 
above-mmtion'd will ftill encreafe at G,fo that the Force of Gravity 
in the Direction G S will check the projeCtile Force which now ads 
in the Line G g, and ftill retard the Planet more. The Angle conti- 
nuing to be obtufe at H and I, the Planet is ftill retarded till it comes 
to A the Aphelion, where its Motion is the floweft of all It may 
perhaps he ohje filed here ; that fince the Angles a A S, b B % c C 

®c. only decreafe half way from AtoY\* and the Angles S P/^ « Ann - 

Yy 2 SF£ 




35 2 j4 Courfe of Experimental 

Left.- V.S F fy S b gj &c. only encreafe half way from P to A j *' the T la* 
fvf^^io m * ^fending towards the Perihelion fhould not encreafe its Veto- 
*i£ 7 . 20 after it is come half way, becaufe then the Angles, as SE? 5 Q?^ 
encreafe again: neither fhould it retard its Motion after it has 
moved half way from P to Aj becaufe the Angles made by the *Di- 
regions of the two Forces no longer encreafe but gradually decreafe. 
Bup then we muft confider that there is another Cattfe of Accelera- 
tion and Retardation which does not depend upon the Quantity of 
the Angle above-mentioned^ but continues to encreafe after the An- 
gles cedfe to diminifh in the Defcent of the Tlanet towards the 
Sum and that Qaufe likewtfe continues to decreafe in the Afcent 
of the Tlanet from the Perihelion to the Aphelion, even after the 
Angles of the Ttireffions of the Forces ceafe to encreafe : and 
thai ■ Cattfe is the diminifh d or encreas'dDtftance of the Central 
Body (or the Sun SJ the Tower of Attraction changing continu- 
ally in a reciprocal "Proportion of the Square of that Diftance. 
If for Example, we would Compare the Velocity of the Tlanet at 
D and at E, we muft compleat the Parallelogram D J 1 E d P of which 
the two^ Sides D ^ and D d reprefent the Force of Gravity and 
the proje Bile Force when the Tlanet is at D; then we mufl alfo 
compleat the Parallelogram E % P e, in which i Eg is greater than 
D c/ 1 in the fame Troportion as Gravity is greater at E than D * 
likewtfe E e muft be greater than D d, in Proportion as the pro- 
jeflile Force by its continual m Acceleration is there alfo become 
greater ; andtho* the Angle ilie is greater than <f Dd, we jhall 
have a greater "Diagonal EP on account of the greater Length of 
the Sides in the Parallelogram e E e P. 

41. To {hew how agreeable the Gravitation of Planets and Co- 
mets (for what we have faid of Planets is as applicable to Comets) 
towards the Sun, is to the Gravitation of heavy Bodies towards 
t PL 25, F. j-^e Earth ; let us take a View of the 21ft Figure f reprefenting a 
long Ellipfe, or the Orbit of a Comet about the Sun S, when ?r re- 
presents the Perihelion. The Semi-Ellipfe 7r a is. the Line in 
which the Motion of the Comet is uniformly retarded^ and the 
Semi-Ellipfe <wr the Line in which the Motion of the Comet is 
uniformly accelerated. Now, if inftead of including the Sun S in 
the Orbit, we fhould from one Part of the Surface of the Sun P r 
projeft a Body upwards, fo that it fhould rife as far as A, its Mo- 
tion would be uniformly retarded till it came to A, where it would 
have its leaft Velocity • then it would turn again and fall in the 

Line 



A Courje of Experimental Philofophy. 



Line A/> accelerating its Motion till it came to taking up juftLed, V.. 
as much Time in its Afcent as Defcent. And this is what we have ^sTSJ 
fhewn concerning the A&ion of Gravity upon Proje£tiles,. abftra£t- 
ing from the Refiftance of the Air. 

4?. But now let us take in the kefiftanceof the Air, and com- 
pare- it with any refifting Medium, to fee what would happen to 
the Planets, if they movM in fuch a Medium. 

We have .fhewn, f that when Bodies move in the Air, they Iole off No. 32. 
their Motion by the Refiftance of the Air, in Proportion to the ^ 340 
Square of their Velocity ; and that that Refiftance hinders falling 
Bodies from accelerating their Motion, -as they would do, if they 
fell in a Vacuum ; becaufe that Refiftance continually taking away 
fomePartof the Velocity, which Gravity fuperadds to the falling 
Body, continually brings the Motion of the Body nearer and near- 
er to a Motion of Equality* Now, if the Planets movM in a re- 
fifting Medium^ fuch as the coeleftial Matter, which the Carte/tans 
fuppofe; the Refiftance of that Matter would hinder a Planet from 
acquiring that Velocity in its Defcent to the Terihelion, which is 
neceifary to make its centripetal Force balance the Force of Gra- 
vity ; for this laft Force would always increafe in Proportion to the 
Square of the decreasM Diftan.ee, let the Medium encompafling the: 
Sun be of what Nature it would; but the centrifugal Force would 
want its proper Increafe, if the Planet wanted its requirM Velocity. 
The Confequence therefore would be, that the Planet would change: 
its Track and come nearer to the Sun, and revolve in a longer El- 
iipfe. The next Revolution, the Planet coming towards the-Teri- 
heiion, and wanting its due centrifugal Force, would be brought 
nearer to the Sun by the Attra&ion (not diminifhM, but increasM, 
becaufe now the "Perihelion would be nearer) ; then again would 
the Eliipfe be changed into a longer, and the next 'Perihelion 
would beftill nearer; till the Planet for want of its due Velocity in* 
a Direction along the Tangent, approaching nearer and nearer 
every Revolution, would at laft fall into the Sun. 

N o w, fince no fuch Thing happens, it is evident, there is no fuch 
v^Mt^ : Medium^ or cmleftial Matter of a Vortex , as the Carteji* 
am fappofe to Be the Caufe of the Motion of the Planets round 
the Sun. So '' far -from that, that fuch a Fluid would deftroy the 
Motion of . tte-<flcinets, as, we have fliewn. 




A Courfe of Experimental Philofophy* 

But what deftroys the Cartefian Hy pothefis at once (as well as 
the Opinion- of thole ancient Philofophers, who fuppofed folidOrbs 
of chriftal to belong to every Planet, and carry it round) is the 
Observation of Comets, which are neither Meteors, as fome of 
the Ancients fuppos'd them, nor Planets ftraying from one Vortex 
to another, as the Cartefians affert ; but Planets moving in very 
excentrick Orbits, which we fhall confider more fully in another 
•.Ann. 8. Place.* Only here we are to obferve, that they move freely to 
and from all Parts of the Heavens ; and therefore there can be no 
chriftal fpherical Shells, which would ftop them ; nor Whirlpools of 
Matter, which would change their Dire&ion by degrees, and at 
laft make them move nearly in the fame Plane as the Planets, whole 
Orbits have all their Planes contained in the Breadth of a Zone of 
a few Degrees, But what is moil contrary to the Cartefian Hy- 
pothefis, is the Motion of a retrograde Comet, fuch as that of the 
Year 1682, which moving from feaft to Weft, was carried dire&ly 
againft the fuppos'd Stream of cceleftial Matter ; and, inftead of ha- 
ving its Motion firft diminilh'd, and then quite ftopp'd, and after- 
wards being carried in a contrary Direftion (which muft ollow, 
when a Body moving from Eaft to Weft falls into a Vortex, whofe 
Matter moves from Weft to Eaft) it accelerated its Motion in its 
Defcent towards the Sun. 

43. Th o' we may very well call the Medium, in which Planets 
move, a Vacuum ; yet, fince Light is propagated thro 7 all the cce- 
leftial Spaces, and fome fine Effluvia may be feparated from the 
Comets and Planets, there will (ftri£tly fpeaking) be fome Refi- 
nance to the Motions of the Planet, tho' not fo much by many 
thoufand times as our Air would make \ and that Refiftance after 
a great Number of Years, muft fo alter the Motion of the Planets, 
■f This is sir as to require the Author of Nature's mending Hand, f If any Al- 
jfaac Neu- teration has been found in their Orbits, tho' ever fo fmalL fince 

Yaw's Opimor. n - t 7 . ? 

See the Que- Altronomers began to make accurate Obfervations (as a great ma- 
'trlftis n ^ a ^ rt ^ at there has) that will be fufficient to fhew, that the 
%tich. World is not eternal, if there were no other Arguments againft 
its Eternity. 

The Sun has been obfervM td have a confiderable Atmofphere • 
as its Surface, on account of the prodigious Heat, muft always be 
throwing out Effluvia, thofe Effluvia (except fuch as are fmall 
enough to become Particles of Light, and be darted off with im- 

menfe 



A Courfe of Experimental Thilofophy. g*£§; 



menfe Velocity) floating about round the Sun's Body muft make a£e£E V* 
Medium, at leaft as denfe as our Air. Now, if a Comet comes -^r^ 
near enough to go into the Sun's Atmofpliere, it will on the ac- 
count of the Refiftance it meets with, come nearer and nearer to 
the Sun every Revolution, and at laft fall into it. Such may in 
Time be the Fate of the Comet obferv'd in i68e, which came fo 
near the Sun as to be, at its ^Perihelion, no farther diftant from the 
Sun's Surface than the 6th Part of the Sun's Diameter. For what 
we know, many a Comet may have fallen into the Sun without our 
Knowledge and Obfervation and perhaps thofe Bodies may ferve 
as frefh Fewelto replenifh the Wafte of the Sun in fupplying the- 
Syftem with Light ; for tho' it has been objected, that a Comet 
would be butafmall Supply, yet if it be as big as the Earth, it 
will be in Diameter the i ooth Part of that of the Sun y that is, ih 
folidity the Ten hundred thoufandth Part; and that may be as> 
much as the Sun in many Years may lofe in Light ; nay, tho' the: x 
Comet fhould be no bigger than the Moon (as moft Comets are 
fuppofed to be of that Bignefs) yet it might ftill be a fufficient 
Supply for the Wafte of Light. 

44. T h o' thefe are but Conje&ures, yet it may not be unac- 
ceptable to the Reader, to fhew by a Scheme, how a Comet, when* 
once it comes in to the Sun's Atmofphere^ will at laft fall into it*. 

Tlate 26. Fig. j; 

Let A BP it be the Orbit of a Comet, S and F its Foci, S the 26. K ii^ 
Sun, and D p> C the Sun's Atmofphere. When from the Ap he li- 
on A the Comet is come towards the 'Perihelion as far as B, the 
Refiftance of the Sun's Atmofpliere hindring fome of the Accele- 
ration, which the Comet ought to have, the Sun's AttraQion will 
give its Orbit more Curvature at the Ver the lion, bring it nearer 
to it felf, and make it come to b inftead of> in its going off, fo 
that it will then have lefs Curvature, the Sun's Attraction, at its 
going off, a£Hng more dire&ly againft the Dire&ion of the projec- 
tile Force. This will make the Ellipfe longer, carry the Aphelion^ 
to A, and make the Focus at /' be farther off from the Sun than 
when it was at F. The next Revolution, when the Comet comes 
down to ft, it will ftill come nearer to the Sun in its ^eribelkn, and 
quit it.at 8 in a new Dire&ion, fo as to go off in an Ellipfe ftill 
longer, whole farther Focus is at $ m& Jphelion at :*j and fo op* 






35^ ji LiOurje .g 



V- -till at laft it comes down to the Sun in the Line a S. But if a Comet 
or Planet moves in the Orbit whofc##a are at the Sun S and at 
f r and whdfe ^Perihelion f is quite out of the Sun's Atmolphere^ 
.the- .Motion of the revolving Body will not be fenftbly diftrfdia 
many thouland ¥ears e 

Other Things relatihg to Aftronomy cannot be well (under- 
flood, till we have explained 

The Third Law of Motion. 

45 r To every A£tion there is always opposed an equal ReaBion ; 
or the mutual Actions of two Bodies upon each other, are always 
vtfkal, and dire Bed to contrary V arts. 

Wft a t e v e r draws or prefles another, is as much drawn or 
preflM by that other. If a Man preffes a Stone with his Finger, 
the Pinger is alfo prefs'd by the Stone. If an Horfe draws a Stone 
tied to a Rope, the Horfe (if I may fo lay) will be equally 
drawn back towards the Stone : For the ftretched Rope, by the 
fame Endeavour to relax and unbend it felf, will draw the Horfe as 
touch towards the Stone, as it does the Stone towards the Horfe, 
and will obftruft the Progrefs of the one as much as it advances 
that of the other. Suppofe, for Example, that the Horfe is able 
to overcome an Obftacle equal to locoifc Weight, preffing againft 
it with his Breaft; when the Horfe draws a Stone of looflb 
"Weight, he will then be able to furmount an Obftacle but of 900 ife 
the Stone taking away from the Force of the Horfe as much as 
^^(»'to ''brhig it felf forward. We muft therefore take care 
rightly ^to underftand the Term as much j and diftinguifli it from as 
far. If a Body ftrikes upon another, and by its Force changes 
the Motion of the other ; that Body alfo ( becaufe of the Equality 
Df the mutual PfelTure) will undergo an equal Change, in its own 
Motion towards the contrary Part. The Changes made by thefe 
Anions are equal, not in the Velocities (unlefs in fuch Cafes as the 
two Bodies have the fame Quantity of Matter) but in the Motions 
or Momenta of the Bodies; that is to fey, if the Bodies are not 
hindered by any other Impediments. For, becaufe the*Motions are 
equally changM, the Changes of Velocities made towards contrary 
Parts, " are reciprocally proportional to the Bodies* This Law 
takes f lace alfo in Attractions* ' 7 late 



A Courfe of Experimental Phihfophy. q^j 

Vlate 16. Fig. 2. ^YV 

46. I f in a large Veflel of Water A B a Loadftone L / be fet 
afloat on a Piece of Cork, and a Piece of Iron or Steel li of the 
fame Weight be likewife fet afloat on another Piece of Cork, they 
will come towards one another and meet at C the middle of their 
pittance ; which fhews, that the Attraction is mutual between the 
Loadftone and the Iron. 

It is well known, that any long Piece of Steel, which has 
had each End drawn over the Poles of a Loadftone, will with one 
End attraft the Pole that gave it the Virtue, but repell the other 
Pole ; and fo likewife with the other End. If then 1/ be the 
touch'd Piece of Steel, whofe End I has receiv'd its Virtue from 
the Pole L of the Stone, and i from the Pole /; the Steel and 
Stone will come together in the manner above-mentioned when I 
is plac'd towards L; but if either i of the Steel, be placed towards 
L o{ the Stone, or / of the Stone towards I of the Steel, and they 
be brought as near to C as the Corks on which they float will al- 
low, then as foon as they are left to themfelves, the Stone and 
Steel will repell one another ; which lhews, that Adion and Re- 
action, or equal and contrary as well in the Repulfions as At- 
traaions. + f Ann g . 

47. AGand.B* are two Boats of equal Bignefs arid Weight *a 2 6.F 0 % 
floating on the Water 'and at reft, at the Diftance G F ; a Man in 

one of them at G pulling a Rope faften'd at F, by pulling will 
bring both the Boats together, and they will meet at C their com- 
mon Center of Gravity, which happens alfo here ( becaufe they 
are equal ) to be the middle of their Diftance f. When the Boats+L - 
are together at C, if the Man pufhes the Boat FB from him, that 
Boat and his own Boat will recede from each other to equal Di- 
ftances from C. But if the Boat F B had been as big again (for 
Example had been FB H) and the common Center of Gravity of the 
two Boats had been at c, the Diftance of the Boats being GF- 
then by the Pull of the Man, the Boats would have met at c the 
biggeft Boat going thro' but half the Space which the leaft would so 
thro' ; likewile if they were pulh'd afunder from the Point c, the Ve- 
locity of their Recefs would be reciprocally proportionable to their 
Mais ; that is, A G would recede as far again as FB H, the common 

'2z Center 



L. 2. 



q $ 8 A Courfe of Experimental Philofophy. 

Left. V. Center of Gravity in both Cafes being at reft, f It is plain here, 
that the Momenta of both Boats will always be equal, tho\ their 
Velocities are only equal when the Boats are fo ; and thefe equal 
Momenta^ whereby the Boats are carried towards contrary Parts, 
fhew that Action and Re-a£tion, in all Cafes where Bodies aft up- 
on one another are equal and contrary. If the Boat A G had been 
clofe to a large Ship, and the Man had pulh'd his Boat off, he 
would have .given as much Motion , to the Ship as to the Boat ; I 
fay, the Ship would have mov*d as much, but.not as far} becaufe 
the Velocity of the Ship being as much lefs as the Ship is bigger 
than the. Boat, would have been infenfible to Sight; and therefore 
tile Vulgar in-fiich a Cafe imagine, that the Ship does not move 
at all ; and much iefs, that when a Man puflies ., againft , the Shore 
to fhove off his 1 Boat, he moyes the wliQle Earth as much as his 
Boat; is mpy'd ; tho' it is certainly true. - In firing a Cannon, the 
I^iofion. of *h^ Cannon backward as; much as 

it puffins the BaH forward, only the Quantity of . Matter being vaft- 
ly more in the Cannon than in the Ball, the Recoil is but of a; 
few Feet, whilft the Ball goes perhaps joooo Feet ; in cpnfider- 
irig the I Recoil we muft'add ' the Frittion of the Carriage of- the; 
Cannon againft the Earth, ^hich; will ftill diminifh the Velocity; 
of ihe ^ann0 s Motion. If the Cannon be faften'd to a Ship, we 
feel only" a : hock as we ftand in the Ship when the Cannon is j 
fir'd , becaufe all the Matter of the Ship beiig added to the recoil- 
ing Cannon, the Velocity diminifhes in Proportion to the Matter 
added to the Cannon, which makes it infenfible to the Sight, and 
only to be felt by a Shock. 

48. Action and Re-acTion are very plainly feen in rowing, 
fwimming and flying ; as for Example, when the Man K in the 
*P1 2 $. f. 4. Boat I K( Fig, 4.*) pulls his Oar, he drives the Water towards H, 
and the Water drives the Boat as much towards D. In fwimming, 
which is nothing but rowing with the Hands and Feet, we are as 
much puffi'd forward by the Water as we puftt the Water back. 
The fame Thing explains the flying of Birds, who are pufh'd for- 
ward by the Re-adion of the Air againft their expanded Wings, 
when they ftrike the Air with them. As for Example, if a Bird 
ftrikes the Air downwards with his Wings, with a Force equal to 
what would raife ioPound, the Re-acijon of the Air will pufli him 
up with the fame Force ; but if the Bird weighs one Pound, the 
Effed of the Re-aaion of the Air will; make the Bird rife with 

Force of only 9 Pound ; that is, the Bird will rife juft as one Pound 

would 



A Courfe of Experimental Philofophy. g§p 

would do tied to a String running over a Pully, by the Fdrce of Le£h V, 
the Defcent of \o Pound at the other End of the String. If the ^V^' 
Bird fhould ftrike the Air only with a Force equal to his own 
Weight, he would for fome time be fufpended in the Air without 
Motion, as we often fee Kites, Hawks, and other Birds of Prey; 

49. The above-mentioned Laws of Motion once underftood* 
the Thtenomena of the Tides will be eafily accounted for ; but to 
make the Matter ftill eafier, let us take the following Confidera- 
tion or Lemma along with us. 

If, when three Bodies are moving after one another the fame 
Way, with the fame Velocity, there be an additional Force im~ 
frefs^d upon each of them, but greater in the Firft, lefs in the 
Second^ and jet lefs in the Third ; their T)iftances from each 
other will continually increafe, t ho' they all continue to move the 
fame way, and all of them fafter than they did before. 

Let us fuppfe the three Boats AG, FB, and tK^ {Fig. . 3> tH.*6-F*3>4. 
and 4.) to be carried along a Streainfron^\A■t^^fds , D, floating 
down with equal Velocity > and that there is but one Man to 
row the Boat AG, two Men to row the Boat FB, and } four 
Men to row the Boat XK. Now whilfi none of the Men row? 
the Boats j as they are carried down by the Stream j continue to 
be at equal Diftances from one another ; fo that if a Man, fit* 
ting in the middlemoft Boat at can with a long Rod reach the 
Head of the hindmoft Boat at G, and the Stern of the forepioft 
Boat at Ij he fhall continue to be able to do it while the Men 
in the Boats do not row ; but, if we fufipofe, that all the Men 
at once begin to row, the Motion of all the Boats towards D 
will be accelerated, but differently ; for the four Men in the fore** 
moft Boat will accelerate it f after towards D than the two Men 
in the middlemoft Boat, and thefe two laft will make their Boat 
go on f after than the Jingle Man in the laft Boat A G y fo that 
the T erf on, who holds a Rod in the middle BoatFB, will no 
longer be able to reach either the Boat that goes before him j or 
the Boat that follows him > hit will be aft to fancy (when he 
does not attend to his own Motion) that the Boat before him 
haft ens away from him, and that the Boat behind him goes back- 
ward. This Confideration will help m to explain the Caufe of 
the Tides, _ 

z 2 50* If ■ 



3<5o A Courfe of Experimental Phibfoghy. 

Left. V. 5c. If the Earth was perfectly fcnooth, without Mountains or 
y/w Vallies, the Sea would make a watery Shell about it, which Shell 
would be concentrick to the Earth, if, no Body was near it, to alter 

*PI. 2 6. f. 5 ..the Figure of this Fluid by its Attra&ion. Let*/ yn ,* r eprefentthe 
Figure of the Earth in fuch a Suppofition, C its Center, and A P LN 
the Surface of the Sea, which is concentrick to the Earth, becaufe 
equally gravitating towards the Center of the Earth in every Part. 
Now, let us coniider, what Effect the Moon at M (CM being a 
Diftance of ^o. Semi-diameters , of the Earth) muft have. Since 
Action and Re-action are, equal, as much as the Moon gravitates 
towards the Sea at L, fo much does the Sea gravitate towards the 
Moon ;.. but as the Sea does alfo gravitate towards C the Center of 
the Earth, with much more Force (as it has 40 times more Mat- 
ter, and is 6p times nearer) the Moon at the Diftance ML at- 
tracting it in a. contrary , Direct ion can only take off from the Gra- 
vitation towards the Earth fo much as amounts to its accelerating 
Force at that Diftance M L. This will make the Water at L 
fwell up to / ; and at the fame Time it will be High- water at A, 
the Water alfo fwelling up to a, on the oppofite Side of the Earth, 
whilft the .Water falls at P and N to fupply the Rife at / and a. 
If we confider the Water at L, the Earth at C (reducing all its 
Weight into its Center of Gravity, as it is not a Fluid to change 
its Shape) and at the Antipodes of L the Water at A, we fhall 
come to the Cafe of the three Bodies, or three Boats in the pre- 
ceding Lemma; for all thefe three gravitate towards the Moon at 
M ; but differently according to their Diftance, in the following 
Proportions. The Water at L is diftant from the Moon M, 59 
Semi-diameters of the Earth ; but the Center of the Earth C is diftant 
from the Moon 60 Semi-diameters ; therefore as much as 360c, the 
Square of the Moon's Diftance from the Center of the Earth, is a grea- 
ter Number than 5481 the Square of 5 9, or the Moon's Diftance from 
the Sea at L ; fo much is the Attraction of the Moon (that is, the ac- 
celerating Force towards the Moon) greater on the Sea at L, than 
the Earth at C, which makes it come forwarder towards the 
Moon to 7; or in other Worda, this makes High- water at / under 
the Moon. There is likewife at the fame Time High- water at 
the Antipodes,, or oppofite Part of the Earth at*?; becaufe the 
Water there being lefs attrafted than the Center of the Earth 
( in the reciprocal Proportion of the Square of the Diftances, that is 
as much as 3.600, the Square of the Diftance of the Center of the 
Earth, is a lefs Number than 3 72 1 the Square of A M = 6 \ the 

Diftance 



A Courfe of Experimental Philofophy. 36 r 



Diftance of the Sea at the Antipodes from the Moon) v iTiuft rife at Ledt. V r 
a by being left behind, or not advancing towards the Moon fofaft w^%^w 
as the Center of the Earth. For as the three Bodies L, C, and 
A, all tend towards the Moon, but L with more Force than C, 
and C with more Force than A, the Diftance C L, as well as the 
Diftance C A, muft increafe from thofe Inequalities of Force a£}> 
ing the fame Way. 

5.T. I have often heard it obje£ted, that it did not feem proba- 
ble, that the Moon fhould raife the Water at one Part of the Earth, 
as L, by attracting the Watdr more than the Earth ; and at the 
fame time raife it at theoppoflte fide of the Earth, as at A, by at- 
tracting it lefs than the Earth ; but the whole Objection will va- 
nifh, by explaining the meaning of the Word to raife the Wateiy 
which here is equivocal. In refpedt of the Earth, what is farther 
removed from the Center of the Earth, is faid to be rais 1 d J> and in 
that Senfe the Water at a is raifed as well as at / - r but in refpe£t 
of the Moon at M, if the Water at L is faid to be rais r d^ becaufe 
it comes to / nearer to the Moon, the Water at A going to 
farther from the Moon, fliould rather be laid to be depre[s r d^ or 
left behind, as it is lefs attracted *than the Earth. If we confider 
the Earth drawn towards M, fo that the Part B a B of its Sur- 
face, is brought to Bee 6, whilft the Water remains at A, or comes 
on towards M more {lowly than the Surface at B there will 
happen the fame Thing to an Inhabit